Study Guide -- Momentum, Center of Mass (Mr. Rogers AP Physics C )

Unit Plan Practice Test Study Guide

Mathematical models

Momentum Impulse
P = mv Imp = DP
Imp = Ft              for constant force


Imp = ∫ F(t) dt
  Note: the area under the F vs. time curve equals the change in an object's momentum.

Newton's 2nd Law

Center of Mass

S F = dP / dt
xcm = (S mixi ) / (S mi ) xcm =1/m  ∫  x dm
ycm = (S miyi ) / (S mi ) ycm = 1/m  ∫ y dm


Thrust = vm dm/dt  

Key Principles

Elastic Collision:
  • momentum is conserved
  • kinetic energy is conserved.
  • The particles do not stick together
Momentum is a vector:

All the rules for vectors apply. For example, when add 2 momentum vectors in different dimensions, you cannot simply sum their magnitudes. You must use vector addition:

P = (Px2 + Py2) 0.5

Inelastic Collision:
  • momentum is conserved
  • kinetic energy is not conserved.
  • The particles stick together
Explosion of moving objects:

If a moving object explodes, the center of mass will continue along the same path as it would have even without the explosion.


Rockets behave similar to exploding devices. In outer space the rocket's center of mass (including its fuel) will remain in the same location. Rocket thrusters must expel mass to move forward.

Impulse and Newton's 3rd Law:

When two objects collide the impulse on one is equal in magnitude but opposite in direction to the impulse on the other. Impulse is a vector and Newton's 3rd law applies to it just like it applies to forces.

Problem Solving Tips: Momentum

Multi-dimensional momentum problems: Think components!
Center of Mass (CM): When calculating the CM, the location of the origin is arbitrary. Always place it in a convenient place that simplifies the problem. Note that the center of mass is like a balance point. If you imagine placing a fulcrum under the CM, the object should look like it is balanced on it.

Example Problems

Ballistic Pendulum: The ballistic pendulum uses a combination of conservation of energy and conservation of momentum to find the velocity of a projectile.  



Momentum Elastic collision Center of Mass
Impulse Inelastic collision  

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