AP physics Momentum and energy

1. AP Phys B
Test Review
Momentum and Energy
4/28/2008

2. Overview
 Momentum
• Center of Mass
• Impulse-Momentum Theorem
• Conservation of Momentum
 Energy
• Work-Energy Theorem
• Conservation of Energy
• Elastic and Inelastic Collisions

3. Momentum
 Momentum
• Momentum is defined as:
• The rate of change of momentum of an object is equal
to the net force applied to the object.
 
p m v=
Σ
∆
∆


F
p
t
=

4. Conservation of Momentum
 Conservation of momentum states that:
the total momentum of an isolated
system of objects remains constant.
• Isolated system: no outside forces acting on
the system
• Tip: Break the momentum of each
component up into horizontal and vertical
components: these are independent of one
another!

5. Collisions and Impulse
 Impulse-momentum theorem defines impulse and says
that the impulse on a system will be equal to the
change in its momentum.
 
F t p∆ ∆=

6. Center of Mass
 The center-of-mass of a collection of particles
if given by the following equation:
• The total linear momentum of a system of particles is
equal to the total mass M of the system multiplied by
the velocity of the center of mass of the system.
• Extended systems use this formulation for Newton’s
Laws too.
x
M
m xC M i i=
1
Σ

7. Work and Energy
 Work is merely a force applied on an object
over a certain distance.
 Kinetic Energy is the energy of motion.
 Potential Energy is the ability of an object to
start/stop motion.
• Gravity: Elastic
W F d= c o s θ
T m v=
1
2
2
U m g h= U k x=
1
2
2

8. Work-Energy Theorem
 This principle states that the work done on an
object is equal to the change in kinetic energy
of an object
W T= ∆

9. Conservation of Energy
 Conservative vs. Non-conservative
Forces
• Friction
 Conservation of Energy: The total energy
of an isolated system cannot change.
• Shift between potential and kinetic energy.

10. Power
 Power is defined as energy over a given time
period.

11. Collisions
 Elastic Collisions
• “Rubber” – things bounce off.
• Both energy and momentum are conserved.
 Inelastic Collisions
• “Gluey” – things stick together
• Only momentum is conserved!

12. Rotational Mechanics
 Radians
 Angular displacement, velocity,
acceleration
 Moment of Inertia
 Torque
 Angular Momentum

13. Simple Harmonic Motion
 Period and Frequency
 Oscillatory Motion
• Springs, Pendulums
• Conservation of Energy
• Position as a function of time
x t A t( ) c o s ( )= ω