The applets and Flash animations listed below are part of the MAP
(**M**odular **A**pproach to **P**hysics)
tutorial at http://canu.ucalgary.ca/. MAP can be used at the high-school,
and first and second-year university levels.

A password may be required to access the MAP tutorial. Please get in touch with Hans Laue (hlaue@ucalgary.ca) if you require the password. The listing below provides direct links (without password protection) to individual applets and FLASH animations from the MAP tutorial. It indicates where in the MAP tutorial the items are used.

All materials in the MAP tutorial or in the listing below are copyright protected. Please get in touch with Hans Laue (hlaue@ucalgary.ca) if you wish to use any of these materials for any purpose other than personal viewing.

The applets are designed to be viewed using the CANU Navigator, the content navigation utility of the MAP system. Since the links in the present file do not access the applets via the CANU Navigator, some of the applets may not get displayed automatically when you click on the link. The link may take you to a directory instead. In this case, click on the file "applet.html" (or, perhaps, "page2.html") in the directory to display the applet.

Most applets have a Help menu to provide information on how to use the applet. To access this information, pull down the Help menu and go to Applet Help. For some applets, Applet Help still has to be made available on the Help menu. The listing below indicates if an applet has Applet Help information available.

In general, the information available from a Help menu under Applet
Help consists of several files, named *Help*, *Assumptions*,
*ShowMe*, and *Lesson*.

*Help*provides information on how to use the applet.*Assumptions*spells out the physical assumptions underlying the applet.*ShowMe*is a guided tour through the applet in the form of exercises.*Lesson*contains a number of exercises to be carried out with the applet that illustrate what can be learned with the applet.

Items indicated by an asterisk (*) are being used also by Alberta Education.

**Introduction to Mechanics**

Motion and Interaction. Item consists of four separate applets and text showing an object carrying out four different motions: one motion that involves no interaction with another object, three motions that do. The applets can help draw attention to the fact that interactions are related to acceleration and that one needs to study acceleration.

__MAP Location__: MAP/Mot'n & Interact'n/Get A Glimpse.

**Errors**

Absolute vs. Relative Error. Item consists of six-page sequence explaining absolute and relative error by means of two applets.

__MAP Location__: MAP/Errors/(Abs/Rel Error)/Explain It.

Systematic vs. Random Error. Item consists of seven-page sequence explaining systematic and random error by means of three applets.

__MAP Location__: MAP/Errors/(Sys/Ran Error)/Explain It.

Propagation of Error. Item consists of six-page sequence explaining error propagation by means of the max-min method. One applet is used to explain the method. Pages 4 and 6 are not completed at this time.

__MAP Location__: MAP/Errors/Propagation of Error/Explain It.

**Vectors**

Blimp Ride Calgary - Edmonton. Flash movie (with sound) illustrates the vector nature of velocity and the vector addition of velocities.

__MAP Location__: MAP/Mathematics/Vectors/Basic Facts/Get A Glimpse.

Basic Vector Attributes. Applet simulates the magnitude and direction of a vector.

__MAP Location__: MAP/Mathematics/Vectors/Basic Facts/Simulate It/Mag'tude and Dir'n.

*Vector Specification. Applet allows four different ways of specifying a vector:

- by magnitude and direction using positive angles only,
- by magnitude and direction using both positive and negative angles,
- by magnitude and direction specifying the angle in terms of compass directions,
- in terms of Cartesian scalar components.

The applet has Help, ShowMe, and Lesson documentation under Applet Help on its Help menu.

__MAP Location__: MAP/Mathematics/Vectors/Basic Facts/Simulate It/Vector Specifa'n.

Scalar Multiplication of Vectors. Applet demonstrating scalar multiplication.

__MAP Location__: MAP/Mathematics/Vectors/Scalar Multiplication/Simulate It.

Two Methods of Vector Addition. Five-page sequential applet with text guides user through construction of the sum of two vectors either by the tip-to-tail or the parallelogram methods.

__MAP Location__: MAP/Mathematics/Vectors/Addition/Simulate It/Two Add'n Methods.

*Addition of Two Vectors. Applet allows user to construct the sum of two vectors by the tip-to-tail or parallelogram methods in a single applet window, thus contracting the previous five-page 'guided tour'.

The applet has Help, ShowMe, and Lesson documentation under Applet Help on its Help menu.

__MAP Location__: MAP/Mathematics/Vectors/Addition/Simulate It/Add Two Vectors.

Addition of Three Vectors. Applet allows user to construct the sum of three vectors. The user is taken through the construction in a five-page sequence.

The applet has Help documentation under Applet Help on its Help menu.

__MAP Location__: MAP/Mathematics/Vectors/Addition/Simulate It/Add Three Vectors.

*Addition of Vectors - Numerical. Applet allows user to add an arbitrary number of vectors that can be specified in one of four ways. (See Vector Specification applet above.) The applet displays the resultant and its numerical attributes in one of four ways.

The applet has Help, ShowMe, and Lesson documentation under Applet Help on its Help menu.

__MAP Location__: MAP/Mathematics/Vectors/Addition/Simulate It/Add'n Quantitative.

Vector Subtraction. Applet allows user to

- draw two vectors,
- find their difference graphically, either by the Add-the-Negative method or the Comparison method,
- compare the difference as drawn by the user to the correct difference.

__MAP Location__: MAP/Mathematics/Vectors/Subtraction/Simulate It.

Scalar Components. Applet allows drawing, changing, and moving a vector and displays the vector's scalar components in a coordinate system whose axes can be rotated.

__MAP Location__: MAP/Mathematics/Vectors/Scalar Components/Simulate It.

Vector Components. Applet demonstrates construction of the vector components of a vector along two perpendicular axes. (This applet is quite incomplete. In the applet's present state, the user cannot draw his/her own vector and the user cannot choose the axes before drawing the components.)

__MAP Location__: MAP/Mathematics/Vectors/Vector Components/Explain It.

Dot Product: Geometric Formulation. Applet simulates the dot product (scalar product) of two vectors in terms of the magnitudes of the two vectors and the angle between them.

__MAP Location__: MAP/Mathematics/Vectors/Dot Product/Simulate It/Geometric.

Dot Product: Analytic Formulation. Applet simulates the dot product (scalar product) of two vectors in terms of the scalar components of the two vectors.

__MAP Location__: MAP/Mathematics/Vectors/Dot Product/Simulate It/Analytic.

Vector Product. Applet displays vector product of two vectors. All three vectors, the two factors and the product vectors, can be dragged at their tips. The vector product is displayed via a 3D perspective drawing. The perspective can be varied by dragging the plane spanned by the two factors. The applet's features are described here.

__MAP Location__: MAP/Mathematics/Vectors/Vector Product/Simulate It.

**Functions**

Sine Function. Applet generates sine function for unrestricted angles by projecting the position of a point moving on a unit circle onto the circle's vertical diameter. The graph of the sine function is drawn.

__MAP Location__: MAP/Mathematics/Functions/Trigonometric/Simulate It/Sine Function.

Trigonometric Functions. Applet generates two basic trigonometric functions, sine and cosine, by projecting the position of a point moving on a unit circle onto the circle's vertical or horizontal diameters. The sine and cosine graphs are drawn. The tangent and cotangent functions can be displayed as well.

__MAP Location__: MAP/Mathematics/Functions/Trigonometric/Simulate It/Trig Functions.

**Kinematics**

Position
Vector. Applet demonstrates the position vector of a ball. The
vector's scalar components relative to a pair of *x*,*y*
axes can be displayed. The origin of the axis can be dragged and the
axes can be rotated by dragging the tips of the axes. This
demonstrates the position vector's dependence on the choice of origin
and the dependence of the vector's scalar components on the
orientation of the axes.

__MAP Location__: MAP/Kinematics/Position/Simulate It.

Displacement as Position Change. Allows user to create two position vectors and shows the displacement as difference of the two.

The applet currently has an un-intuitive interface that needs to be improved.

__MAP Location__: MAP/Kinematics/Displacement/Position Change/Simulate It.

*Displacement vs. Distance Traveled. Applet Shows Initial And Final Positions, Displacement, And Distance Travelled For A Ball Moved From One Point To Another.

The applet has Help, ShowMe, and Lesson documentation under Applet Help on its Help menu.

__MAP Location__: MAP/Kinematics/Displacement/Disp't vs Dist'ce/Simulate It.

Stopwatch The applet simulates a very accurate stopwatch, with minimal delay between clicking the Start/Stop button and the response of the watch.

The applet has Help and Assumptions documentation under Applet Help on its Help menu.

__MAP Location__: MAP/Kinematics/Time/Simulate It/Stopwatch.

Timer Stopwatch The applet simulates both a stopwatch and a timer, with minimal delay between clicking the Start/Stop button and the response of the clock.

The applet has Help and Assumptions documentation under Applet Help on its Help menu.

__MAP Location__: MAP/Kinematics/Time/Simulate It/Timer Stopwatch.

*Average Speed vs. Average Velocity. Applet determines the average speed and average velocity of a ball as the ball is moved from one point to another.

The applet has Help, ShowMe, and Lesson documentation under Applet Help on its Help menu.

__MAP Location__: MAP/Kinematics/Speed/Average/Simulate It/(Distance/Time).

*Average Speed as Weighted Average. The applet simulates that the average speed of an object during a time interval is the weighted average of the object's speeds in portions of that time interval.

The applet has Help, ShowMe, and Lesson documentation under Applet Help on its Help menu.

__MAP Location__: MAP/Kinematics/Speed/Average/Simulate It/Weighted Average.

Velocity as Time-rate-of-change of Position. The applet controls the motion of a car via a velocity dial, displays the position and velocity vectors, and allows the motion to be viewed (repeated) in either position or velocity space. Tracks in position and velocity space can be displayed.

__MAP Location__: MAP/Kinematics/Velocity/Basic Facts/Simulate It.

Acceleration as Time-rate-of-change of Velocity. The applet controls the motion of a car via an acceleration dial, displays the position and velocity vectors, and allows the motion to be viewed (repeated) in either position or velocity space. Tracks in position and velocity space and the position and velocity vectors can be displayed.

__MAP Location__: MAP/Kinematics/Acceleration/Instantaneous/Simulate It.

*One Ball. Applet simulates motion of a ball in the earth's gravitational field, with or without air resistance. Shows projections of ball onto the x and y axes. Target can be set. Acceleration due to gravity can be varied.

The applet has Help, Assumptions, ShowMe, and Lesson documentation under Applet Help on its Help menu. The documentation also includes a lesson on motion with air resistance.

__MAP Location__: MAP/Kinematics/Acceleration/Due to Gravity/Simulate It/One Ball: Sim'n.

*One Ball - No Air Resistance. Same as the preceding applet without the options of adding air resistance and varying the ball's mass.

The applet has Help documentation under Applet Help on its Help menu.

__MAP Location__: MAP/Kinematics/Acceleration/Due to Gravity/Simulate It/One Ball - No Air.

*Two Balls. Similar to preceding two applets, but with two balls whose parameters can be controlled separately: initial positions and velocities. Ball 2 can be made subject to air resistance and can have its mass varied.

The applet has Help, Assumptions, ShowMe, and Lesson documentation under Applet Help on its Help menu.

__MAP Location__: MAP/Kinematics/Acceleration/Due to Gravity/Simulate It/Two Balls.

Monkey and Hunter. Same as preceding Two Balls applet, but set up for the Monkey and Hunter demonstration and without air resistance.

__MAP Location__: MAP/Kinematics/Acceleration/Due to
Gravity/Simulate It/Monkey and Hunter.

Acceleration in Circular Motion. The applet simulates the position, velocity, and acceleration vectors in circular motion, either motion with constant speed or changing speed. In an Incremental Mode, the applet simulates the changes in the position and velocity vectors during time steps whose size can be varied.

The applet has Help, Assumptions, and ShowMe documentation under Applet Help on its Help menu.

__MAP Location__: MAP/Kinematics/Acceleration/Radial (centripetal)/Simulate It.

*Planet Motion 1. Applet simulates the motion of a planet around the sun. The orbit's eccentricity and semi-major axis can be varied. The values of various quantities related to the motion are printed out. The sun's velocity can be varied, thus simulating different inertial reference frames. The velocity of the planet relative to the lab frame, its velocity relative to the sun, and the velocity of the sun relative to the lab frame can be displayed as vector arrows and dragged to verify the Galilean velocity addition theorem.

The applet has Help, Assumptions, ShowMe, and Lesson documentation under Applet Help on its Help menu.

__MAP Location__: MAP/Kinematics/Acceleration/Due to
Gravity/Simulate It/Planetary Motion/Planet Motion 1.

Planet Motion 2. Same as the previous applet except that the energy and angular momentum of the planet can be varied, controlling the orbit that way.

__MAP Location__: MAP/Kinematics/Acceleration/Due to
Gravity/Simulate It/Planetary Motion/Planet Motion 2.

Physical Pendulum. Applet simulates pendulum motion and displays

- the forces acting on the pendulum (Button 1)
- the instantaneous velocities and acceleration of the pendulum bob
- pertinent data (Button 3).

The pendulum's length and starting position can be chosen by dragging the bob. The bob's radius can be adjusted.

__MAP Location__: MAP/Kinematics/Acceleration/Apply It/Pendulum
Motion/Simulate It.

*Simple Harmonic Motion of a Weighted Spring. The applet simulates the shm of a weight suspended from a spring. The motion is shown to be identical to projected uniform circular motion, and graphs of displacement, velocity, and acceleration vs. time are generated.

The applet has Help, Assumptions, ShowMe, and Lesson documentation under Applet Help on its Help menu.

__MAP Location__: MAP/Simple Harm. Mot'n/Basic Facts/Simulate
It/Weighted Spring.

*Simple Harmonic Motion of a Simple Pendulum. The applet simulates the motion of a simple pendulum and shows it to be approximated closely by projected uniform circular motion. Graphs of displacement, velocity, and acceleration vs. time are generated.

__MAP Location__: MAP/Simple Harm. Mot'n/Basic Facts/Simulate
It/Simple Pendulum.

**Reference Frames**

*Rolling Motion. Applet simulates the motion of a point fixed on a rolling wheel.

The wheel is rolling on an inner core whose radius can be varied. The radial distance of the point from the center of the wheel can be varied as well, giving rise to various kinds of cycloidal paths, including a cusp-like path if the point is on the perimeter of a wheel that is rolling on its perimeter. The velocities of the point relative to the lab, the velocity of the point relative to a frame moving with the center of the wheel, and the velocity of the wheel relative to the lab can be displayed. The velocity vector of the wheel relative to the lab can be dragged to demonstrate that the three velocities satisfy the Galilean velocity addition theorem.

__MAP Location__: MAP/Reference Frames/Inertial Frames/Galilean
Relat'y/Gal'n Kinematics/Simulate It/Rolling Motion.

*Planet Motion 1. Applet simulates the motion of a planet around the sun. The orbit's eccentricity and semi-major axis can be varied. The values of various quantities related to the motion are printed out. The sun's velocity can be varied, thus simulating different inertial reference frames. The velocity of the planet relative to the lab frame, its velocity relative to the sun, and the velocity of the sun relative to the lab frame can be displayed as vector arrows and dragged to verify the Galilean velocity addition theorem.

__MAP Location__: MAP/Reference Frames/Inertial Frames/Galilean
Relat'y/Gal'n Kinematics/Simulate It/Planet Motion 1.

Planet Motion 2. Same as the previous applet except that the energy and angular momentum of the planet can be varied, controlling the orbit that way.

__MAP Location__: MAP/Reference Frames/Inertial Frames/Galilean
Relat'y/Gal'n Kinematics/Simulate It/Planet Motion 2.

Slingshot Effect. Applet shows a space probe moving around Jupiter. One can see how the size of the slingshot effect depends on Jupiter's velocity.

__MAP Location__: MAP/Reference Frames/Inertial Frames/Galilean
Relat'y/Gal'n Kinematics/Simulate It/Slingshot Effect.

Rotating Reference Frame. Applet simulates what a constant-velocity motion (constant velocity relative to the Lab frame) looks like from a uniformly rotating frame.

__MAP Location__: MAP/Reference Frames/Non-Inert'l
Frames/Simulate It.

**Forces**

Box on Table. The applet provides practice with free-body diagrams and Newton's Third Law. The applet examines the forces exerted by the three parts of a physical system on each other. The system consists of a box resting on a table which in turn is resting on the surface of the earth.

The applet has Help, Assumptions, and ShowMe documentation under Applet Help on its Help menu.

__MAP Location__: MAP/Force/Newton's Third Law/Simulate It/Box on Table.

Force in Projectile Motion. This is basically the One-Ball projectile motion applet listed under Kinematics above, but with a couple of additions: (a) the gravitational force acting on the ball and (b) the ball's kinetic and gravitational potential energy. The applet assumes air resistance to be zero.

The applet has Help, Assumptions, and ShowMe documentation under Applet Help on its Help menu.

__MAP Location__: MAP/Force/Gravitational/Simulate It/Projectile Motion.

*Forces of Gravity and Air Resistance. This is the One-Ball projectile motion applet listed also under Kinematics above. The applet displays the forces due to gravity and air resistance acting on the ball and allows the user to vary the magnitude of the acceleration due to gravity and the ball's mass and drag coefficient.

__MAP Location__: MAP/Force/Newton's Sec'd Law/Simulate It/Gravity & Air.

*Weight and Orbits. The applet shows projectile motion and satellite motion in the earth's gravitational field. The projectile's or satellite's initial position and velocity can be varied. The viewpoint can be changed from a point close to the earth's surface to a point far from the earth's surface. The gravitational force acting on the projectile or satellite is simulated.

__MAP Location__: MAP/Force/Gravitational/Simulate It/Weight and Orbits.

*Block on Springs. The applet simulates the normal force exerted on a block resting on springs that in turn are supported by a platform that can move vertically with acceleration. One can view the motion both from the Lab frame and the block's frame (elevator frame). The applet simulates "apparent weight" as registered by a bathroom scale in an elevator.

The applet has Help, ShowMe, and Lesson documentation under Applet Help on its Help menu.

__MAP Location__: MAP/Force/Newton's Sec'd Law/Simulate It/Block on Springs.

Block on an Accelerating Incline. The applet shows the motion of a block on an incline with or without friction. The incline can be set to be either at rest or accelerating horizontally. The forces acting on the block and three accelerations relevant to this situation can be displayed. All vectors can be arranged to demonstrate that Newton's second law is satisfied and that the accelerations satisfy a" Galilean" (non-relativistic) acceleration transformation.

The motion can be observed either in the Lab or the Ramp (Incline) frame. The latter is a non-inertial frame when the incline is accelerating, and the corresponding fictitious force acting on the block can be displayed.

__MAP Location__: MAP/Force/Newton's Sec'd Law/Simulate It/Accel'ing Incline.

*Fletcher's Trolley. The applet simulates a Fletcher's Trolley apparatus (a horizontally moving block connected via a pulley to a vertically moving block). The free-body diagrams for the two blocks and data on the system's acceleration and string tension can be displayed.

__MAP Location__: MAP/Force/Newton's Sec'd Law/Simulate It/Fletcher's Trolley.

Static and Kinetic Friction. The applet simulates a block on a horizontal surface with friction. Both static and kinetic friction are simulated. An applied force is acting on the block.

The applet has Help, Assumptions, and ShowMe documentation under Applet Help on its Help menu.

__MAP Location__: MAP/Force/Friction/Simulate It/Block on Table.

Net Force in Circular Motion. The applet simulates the net force acting on a particle in circular motion, as well as the particle's position, velocity, and acceleration vectors. Motions with either constant speed or changing speed are possible.

The applet has Help, Assumptions, and ShowMe documentation under Applet Help on its Help menu.

__MAP Location__: MAP/Force/Newton's Sec'd Law/Simulate It/Circular Motion.

*Colliding Planets. The applet illustrates Newton's Third Law by simulating the forces acting on two gravitationally interacting bodies. The masses of the bodies can be varied. The applet simulates the forces, velocities, momenta, and energies as the bodies move towards each other.

__MAP Location__: MAP/Force/Newton's Third Law/Simulate It/Colliding Planets.

Forces in Binary Star System. The applet simulates the motion of two stars revolving around each other and shows that the forces the stars are exerting on each other are at all times equal in magnitude and opposite in direction. (Newton's third law.)

The applet has Help, Assumptions, and ShowMe documentation under Applet Help on its Help menu.

__MAP Location__: MAP/Force/Gravitational/Simulate It/Binary
Star System.

*Particle in Electric Field. The applet simulates the motion of a charged particle in a uniform electric field.

__MAP Location__: MAP/Force/Electromagnetic/Simulate It/P'cle in E-field.

One, two or twelve particles in Electric Field. The applet simulates the motion of one, two, or twelve charged particles in a uniform electric field. (The applet is similar to the preceding one, but allows a choice of one, two, or twelve particles moving in the field.)

__MAP Location__: MAP/Force/Electromagnetic/Simulate It/P'cles in E-field.

Charged Particle in Capacitor. The applet simulates the motion of a charged particle in the uniform electric field inside a parallel-plate capacitor, displays the electric force acting on the particle and the particle's potential and kinetic energies.

The applet has Help, Assumptions, and ShowMe documentation under Applet Help on its Help menu.

__MAP Location__: MAP/Force/Electromagnetic/Simulate
It/Capacitor and MAP/Energy/Work-Kin. En. Th'm/Simulate
it/Capacitor.

*Magnetic Force. The applet simulates the motion of a charged particle in a magnetic field.

__MAP Location__: MAP/Force/Electromagnetic/Simulate It/P'cle in B-field.

*Thomson's e/m Measurement. Applet allows determination of the ratio of e/m of a charged particle by measuring the deflection of the particle in crossed electric and magnetic fields and either pure electric or magnetic fields.

__MAP Location__: MAP/Force/Electromagnetic/Simulate It/Thomson Experiment.

**Fields and Potentials**

*Weight and Orbits. This applet is also listed under Force above. The applet shows projectile motion and satellite motion in the earth's gravitational field. The applet can display the satellite's acceleration (orange arrow), which is equal to the gravitational field vector at the position of the satellite.

__MAP Location__: MAP/Field/Gravitational/Simulate It/Weight and Orbits.

*Inverse
Square Law. The applet simulates the gravitational field both
outside and inside a sphere of uniform mass density. The field is
proportional to 1/*r*^{2} outside the sphere and
proportional to *r* inside the sphere.

The applet has a graviational and an electric mode. In the electric mode, the applet simulates the electric field outside and inside a uniformly charged sphere.

__MAP Location__: MAP/Field/Gravitational/Simulate It/Uniform Sphere.

*Electric Field and Potential Due to a Point Charge. The applet simulates the electric field lines and the equipotential lines (curves) accompanying an electric point charge.

__MAP Location__: MAP/Field/Electric/P't Charge Field/Simulate It.

*Electric Field and Potential Due to Two Point Charges. The applet simulates the electric field lines and the equipotential lines resulting from two point charges. By setting the charges to equal magnitude and opposite sign, one can use the applet to simulate a dipole field and potential.

__MAP Location__: MAP/Field/Electric/Dipole Field/Simulate It.

*Electric Field Due to Charges on a Straight Line. The Applet simulates the electric field of one or several electric point charges arranged along a straight line or the field of an infinitely extended straight line charge.

__MAP Location__: MAP/Field/Electric/Line Charge Field/Simulate It.

*Potential in Uniform Field. The applet simulates the electric potential at different points in a uniform electric field. It displays electric field lines and lines of constant potential.

__MAP Location__: MAP/Energy/Potential Energy/Simulate It/Uniform El. Field.

*Potential in Non-Uniform Field. The applet simulates the electric potential at different points in the electric field created by a point charge. It displays electric field lines and lines (circles) of constant potential.

__MAP Location__: MAP/Energy/Potential Energy/Simulate It/Nonunif'm El. F'ld.

*Current and Magnetic Field. The applet simulates the magnetic field due to current elements along a straight line and due to an infinitely extended straight-line current.

__MAP Location__: MAP/Field/Magnetic/Straight Wire/Simulate It.

*Magnetic Field Due to Current Loops. The applet simulates the magnetic field due to current in one or several coaxial circular loops.

__MAP Location__: MAP/Field/Magnetic/Current Loops/Simulate It.

**Momentum**

*Momentum Conservation. Applet shows two skaters pushing away from each other or two blocks exploding away from each other.

__MAP Location__: MAP/Force/Newton's Third Law/Simulate It/Skaters and Blocks.

Collision of Two Balls. Flash animation of the collision of two balls.

__MAP Location__: MAP/Momentum/Conservation/Explain It/Ball Collision.

Derivation of the Law of Momentum Conservation. Flash animation that goes through the derivation of the law of momentum conservation in head-on collisions step-by-step. The animation is accompanied by a spoken commentary that requires speakers.

__MAP Location__: MAP/Momentum/Conservation/Explain It/Derivation.

**Energy**

*The Concept of Energy and Energy Conservation. The applet simulates several basic properties of energy by means of colored blocks representing 1 J of energy each that can be moved in and out of a system and be converted into different forms of energy (different color). The total number of blocks (total energy) counting blocks both inside and outside the system remains always the same.

__MAP Location__: MAP/Energy/Basic Facts/Simulate It.

*Rolling Objects on an Incline. Objects of various shapes can be made to either roll or slide down an incline. The applet demonstrates which ones are fastest. The different forms of energy, translational kinetic, rotational kinetic, and potential at a given instant are indicated by colored blocks. The values are printed out as well.

__MAP Location__: MAP/Energy/Energy Conserv'n/Simulate It/Energy Race.

Energy in Projectile Motion. This is basically the One-Ball projectile motion applet listed under Kinematics above, but with a couple of additions: (a) the gravitational force acting on the ball and (b) the ball's kinetic and gravitational potential energy. The applet assumes air resistance to be zero.

The applet has Help, Assumptions, and ShowMe documentation under Applet Help on its Help menu.

__MAP Location__: MAP/Energy/Wk-Kin Energy Thm/Explain
It/Examples, Pages 2 and 4, and MAP/Energy/Wk-Kin Energy Th'm/Simulate
It/Free Fall and MAP/Energy/Wk-Kin Energy Thm/Simulate It/Projectile
Motion.

*Energy and Orbits. The applet shows projectile motion and satellite motion in the earth's gravitational field. The gravitational potential energy of the projectile-earth system or satellite-earth system along with the projectile's or satellite's kinetic energy and the total mechanical energy of the system are simulated. The projectile's or satellite's initial position and velocity can be varied. The viewpoint can be changed from a point close to the earth's surface to a point far from the earth's surface, best for satellite motion.

__MAP Location__: MAP/Energy/Energy Conservat'n/Simulate It/Energy and Orbits.

Energy in Binary Star System. The applet simulates the motion of two stars revolving around each other and the attending changes in the potential and kinetic energies of the binary-star system.

The applet has Help, Assumptions, and ShowMe documentation under Applet Help on its Help menu.

__MAP Location__: MAP/Energy/Wk-Kin Energy Thm/Explain
It/Examples, Page 12, and MAP/Energy/Wk-Kin Energy Thm/Simulate
It/Binary Stars.

Energy of Charged Particle in Capacitor. The applet simulates the motion of a charged particle in the uniform electric field inside a parallel-plate capacitor, displays the electric force acting on the particle and the particle's potential and kinetic energies.

The applet has Help, Assumptions, and ShowMe documentation under Applet Help on its Help menu.

__MAP Location__: MAP/Energy/Wk-Kin Energy Thm/Explain
It/Examples, Page 6, and MAP/Energy/Work-Kin. En. Th'm/Simulate
it/Capacitor.

Work and Kinetic Energy in Circular Motion. The applet simulates uniform and non-uniform circular motion of a masspoint, the masspoint's velocity and acceleration, the net force acting on the mass point, and the masspoint's kinetic energy. Simulated also are the radial (centripetal) and tangential components of the acceleration and force.

The applet has Help, Assumptions, and ShowMe documentation under Applet Help on its Help menu.

__MAP Location__: MAP/Energy/Wk-Kin Energy Thm/Explain
It/Examples, Page 8, and MAP/Energy/Work-Kin. En. Th'm/Simulate
it/Circular Motion.

Work and Kinetic Energy. The applet displays the work done on a ball while the ball is moving subject to a force. The force acting on the particle can be controlled by dragging a force vector. The motion can be replayed and gone through step-by-step, both forward and backward. The work done in each step is calculated and the kinetic energies at the beginning and end of the step displayed. Students can verify that the work done is equal to the kinetic energy change in each step. Forces and displacements necessary to calculate the work done are printed out. The initial velocity vector can be dragged out of the ball, and the ball can be dragged to a suitable initial position. The applet can be run in 1D or 2D.

The applet has Help, Assumptions, and ShowMe documentation under Applet Help on its Help menu.

__MAP Location__: MAP/Energy/Wk-Kin Energy Thm/Explain
It/Examples, Page 10, and MAP/Energy/Work-Kin. En. Th'm/Simulate
it/Variable Force.

SHM - Spring Energy. The applet demonstrates energy conservation for a weighted vertical spring performing simple harmonic motion.

The applet has Help, Assumptions, ShowMe and Lesson documentation under Applet Help on its Help menu.

__MAP Location__: MAP/Energy/Energy Conserv'n/Simulate It/Weighted Spring.

SHM - Pendulum Energy. The applet simulates the motion of a simple pendulum and energy conservation in this system.

The applet has Help, Assumptions, ShowMe and Lesson documentation under Applet Help on its Help menu.

__MAP Location__: MAP/Energy/Energy Conserv'n/Simulate It/Quant've Pendulum.

Conversion of Mechanical Energy into Internal Energy. The applet simulates a block on a horizontal surface with friction. An applied force is acting on the block, and changes in the block's kinetic energy and in the internal energy of the block-table system are graphically displayed, along with the work done on the block by the applied force.

The applet has Help, Assumptions, and ShowMe documentation under Applet Help on its Help menu.

__MAP Location__: MAP/Energy/Thermal Energy/Explain It.

*Fletcher's Trolley. Applet demonstrates energy conservation for a Fletcher's Trolley apparatus. The masses of the two blocks and of the pulley can be varied.

__MAP Location__: MAP/Energy/Energy Conserv'n/Simulate It/Fletcher's Trolley.

*Potential Energy in Uniform Field. The applet simulates the electric potential energy of a charged particle in a uniform electric field as well as the particle's kinetic energy. It simulates the motion of the charged particle in the field and attending energy changes.

__MAP Location__: MAP/Energy/Potential Energy/Simulate It/Uniform El. Field.

*Potential Energy in Non-Uniform Field. The applet simulates the electric potential energy of a charged particle in the electric field created by a charged point source. It simulates the particle's motion in the electric field and the attending changes in the particle's potential and kinetic energies.

__MAP Location__: MAP/Energy/Potential Energy/Simulate It/Nonunif'm El. F'ld.

**Rotation**

Angle. Applet simulates angles and the radian measure of an angle.

__MAP Location__: MAP/Kinematics/Angle/Simulate It.

Angular Velocity. Applet illustrates angular velocity for three kinds of motion: straight-line, circular, parabolic. The point relative to which the angle is defined can be varied. A graph of angular velocity vs. time is displayed.

__MAP Location__: MAP/Kinematics/Angular Velocity/Simulate It/Moving Car.

*Rolling Motion. Same applet as under Reference Frames above.

__MAP Location__: MAP/Reference Frames/Inertial Frames/Galilean
Relat'y/Gal'n Kinematics/Simulate It/Rolling Motion.

Lever Arm. Collection of five applets demonstrating various aspects of the lever arm, both qualitative and quantitative.

__MAP Location__: MAP/Torque/Lever Arm/Simulate It.

Torque About An Axis. Collection of five applets. The first applet simulates qualitative aspects of the concept of a torque about an axis, and the remaining four illustrate four different ways of calculating the torque about an axis.

In all five applets the forces can be varied in magnitude and direction by dragging the tips of the force vectors. The point at which a force is acting can be changed by dragging the force vector somewhere other than at its end points, and the location of the rotation axis can be changed by dragging as well.

The qualitative applet is intended to show the sense of rotation induced by the acting force(s) and the net torque is displayed at every instant of the motion. The motion is not realistic in the sense that it proceeds with constnt angular velocity. The motion stops when the net torque is zero. (The applet seems to malfunction when it is run after certain manipulations with the third applet. Needs to be fixed.)

__MAP Location__: MAP/Torque/About an Axis/Simulate It.

Physical Pendulum. Same applet as under Forces above.

__MAP Location__: MAP/Torque/About an Axis/Apply It/Physical Pendulum.

Leaning Tower. The applet simulates how varying the tilt angle of a tower will eventually lead to the toppling of the tower. The free-body diagram for the tower can be displayed, showing the gravitational and normal forces acting on the tower. The point of effective action of the normal force shifts with the tilt angle. It can be seen that the tower falls when this point lies outside the tower's base.

__MAP Location__: MAP/Torque/Equilibrium/Apply It/Leaning Tower.

Toppling Block On Accelerating Trolley. The applet simulates the toppling of a block that is standing on a horizontally accelerating trolley, if the acceleration is sufficiently large.

The buttons need to be adjusted. One can display the free-body diagram for the block and can see that the point at which the normal force is acting on the block shifts with a change in acceleration. As the acceleration exceeds a certain value, the point at which the normal force would be acting is beyond the base of the block and the block topples. The block's initial velocity can be varied as well and can be seen not to affect the block's toppling.

__MAP Location__: The applet's interface needs work and the
applet is currently not available in MAP. The eventual location will
be at MAP/Torque/Newton II Rot'l/Simulate It/Toppling Block.

Skidding Wheel. The applet simulates the skidding and rolling motion of a wheel that is propelled onto a horizontal track. The buttons need to be adjusted, but their tool tips can be read.

The track's friction can be varied. The initial speed of the wheel can be varied. The wheel skids at first and then starts rolling. One can study how long it takes for the wheel to change from skidding to rolling as a function of the initial speed of the wheel and coefficient of kinetic friction between the wheel and the track. The path of a point on the wheel can be displayed and be seen to change shape as the wheel goes from skidding to rolling.

__MAP Location__: MThe applet's interface needs work and the
applet is currently not available in MAP. The eventual location
will be at MAP/Torque/Newton II Rot'l/Simulate It/Skidding Wheel.

Balancing A Broom. The applet simulates an accelerating person who is trying to balance a broom on his outstretched hand. The person's acceleration and the position of his hand can be varied.

The buttons need to be adjusted, but the tool tips can be read.

__MAP Location__: The applet's interface needs work and the
applet is currently not available in MAP. The eventual location
will be at MAP/Torque/Newton II Rot'l/Simulate It/Balancing Broom.

**E&M**

*Electric Circuit Lab. Applet allows construction of electric circuits containing batteries, resistors, light bulbs, switches, ammeters and voltmeters. The parameters, like battery emf's and internal resistances, resistance values, etc., can be set to arbitrary values. The applet calculates all relevant quantities in the various branches of the circuit: currents, potential differences, potentials at a point, power dissippated. More than one circuit can be constructed simultaneously.

__MAP Location__: MAP/Electric Circuits/Basic Facts/Simulate It/Practice.

Electric Circuit Lab Demonstration. 14-page lesson explaining and demonstrating the features of the preceding Electric Circuit Lab applet, along with some basic circuit concepts.

The lesson is accompanied by a sound track. Speakers are needed when playing the sound track.

__MAP Location__: MAP/Electric Circuits/Basic Facts/Simulate It/Demo.

**Other E&M Applets**. There are other applets from the E&M
area under several of the preceding headings. See the sections on

__Force__for the motion of a charged particle in electric or magnetic fields,__Fields and Potentials__for the simulation of electric fields and potentials and for the simulation of magnetic fields,__Energy__for the potential energy of a charged particle in an electric field.