AP Phys BTest Review

Momentum and Energy

4/28/2008

Overview

Momentum• Center of Mass

• Impulse-Momentum Theorem

• Conservation of Momentum

Energy• Work-Energy Theorem

• Conservation of Energy

• Elastic and Inelastic Collisions

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

F

p

t

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!

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

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.

xM

m xCM i i1

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 Fd cos

T m v1

22

U mgh U kx1

22

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

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.

Power

Power is defined as energy over a given time period.

Collisions

Elastic Collisions• “Rubber” – things bounce off.

• Both energy and momentum are conserved.

Inelastic Collisions• “Gluey” – things stick together

• Only momentum is conserved!

Rotational Mechanics

Radians Angular displacement, velocity,

acceleration Moment of Inertia Torque Angular Momentum

Simple Harmonic Motion

Period and Frequency Oscillatory Motion

• Springs, Pendulums

• Conservation of Energy

• Position as a function of time

x t A t( ) cos( )