Wolfram Demonstrations / mathematica simulations

derivative: (i) tangent vs. secant; (ii) tangent

integral: (i) single function; (ii) multiple functions

(linear) motion graphs

projectile motion: 3D: dynamic; static / me: excel & rotatable graph;

2D / trajectory as a function of angle; as preceding with variable height

relate unit circle & sin, cos, & tan; alt

vectors - dot product

conservation of mechanical energy

GPE of various objects at different locations

KE vs PE of falling object

relate PE, KE, ME - sling shot

gravity / spring relate PE, KE, ME (me)

relate PE and force (me; adapt)

relate ME, PE, KE, and position for spring system ("good", but subtile)

vertical circular motion; PE, KE, velocity

center of mass

system of n objects

translational / rotational motion of wrench

translation / rotation motion of dumb bell

exploding projectile

person walking on boat


elastic / inelastic - adjust degree of elasticity, velocity, and mass; plot of velocity vs time

elastic - 1 or 2- d: 1 (adjust m; time); 2 (relative m; time); 3 (adjust m & v)


axis of rotation

vectors - cross product

Kepler's laws

oscillation unit

behavior of the function: A cos (b t + c)

effect of amplitude, period, & phase on graph (nay)

simple harmonic motion / vertical spring oscillation

torsion pendulum


vector addition

2D circular / ellipitical motion; show velocity & acceleration vectors

mass on a spring; oscillations

vector - from physics cs, and math viewpoints

physics aviary


uniform circular motion

centripal acceleration: relate velocity and delta velocity - see drawing & Khan video

bank turn - video of car / bus (alt)

vertical circular motion - video of person running; Khan academy (partial analysis)


images: pulley / tension

drag force - terminal velocity - me (*.nb); link

rotational motion / angular momentum

rotational inertia (follow links on site)

video: spinning skater (~ 1 "); rotating person with spinning wheel (~ 3") & role of torque (~ 5 "); spinning / diving teacher (~ 9")

ophysics - geobra animation / simulation

relate circular motion & oscillation

textbook resource - simulation / animation

ch.8 conservation of mechanical energy

relate ME, KE, PE: spring, pendulum, arbitrary


center of mass

Newton's cradle - conservation of momentum / kinetic energy\

race rolling ring vs cylinder

ch. 15 oscillations

behavior of cos (*.nb)

simple harmonic motion & uniform circular motion;

1 (animation: sin);

2 (animation (spring oscillation ?): sin or cos);

3 (series of images -> cos);

4 (animation (provides step-wise changes in motion): sin; uniform circular motion, simple harmonic motion, spring oscillation)

relate circular motion & oscillation: ophysics (x-, v-, a- vs time graphs); youtube


read about banked turn - wikipedia

Developing the Energy Concepts in Introductory Physics

Energy & the Confused Student 1: work


frame of reference (video; ~ 27")

ch. 4 planar motion ppt slides

interial vs noninterial frame of reference; apparent weight (ex): link; # 36 - 39; answer key

ch. 8 conservation of mechanical energy ppt slides

center of mass using calculus; 1; 2

center of mass; walk on boat 1

cross product

ap classroom - past MC & FR questions. as a concept could be "integrated" into another concept, the number of MC or FR does not necessarily reflect the potential weigth of that concept.

topics MC FR
link link
1b. Kinematics - Motion in Two Dimensions [18 MC] link  
2. link link
3. ; ; ; link link
4. Center of Mass; ; link link
5. ; ; [20 MC; 13 FR] link link
6. Simple Harmonic Motion, Springs, and Pendulums [13 MC; 15 FR] link link
7. ; link link
2017 ap physics c - mechanics -- link (use as a practice test)