Chapter 9 Momentum and Its Conservation

9.1 Impulse and Change In Momentum

Momentum and Impulse

Momentum is the product of the mass and the velocity of a body. It is a vector quantity.

p = mv (Units of momentum are kilogram-meter/second)

From Newtons second Law:

F = ma = mdv/dt

Therefore:

Fdt = mdv

Impulse is the product of the force and the time interval over which it acts

(Units for impulse are Newton-seconds)

dp = mdv

Therefore:

Fdt = dp

Impulse-Momentum theorem: The Impulse is equal to the change in Momentum.

Angular Momentum

Angular momentum is the product of an objects mass, velocity, and distance from center of rotation.

<p = mvd

9.2 The Conservation of Momentum

Newtons Third Law and Momentum

The impulse-momentum theorem is another way of stating Newtons third law.

Fdt = dp

System a defined collection of objects

Isolated system

1. objects neither enter nor leave

2. no external forces act on it

In an Isolate system the net change in momentum is zero.

pA1 + pB1 = pA2 + pB2

Law of Conservation of Momentum

The momentum of any closed, isolate system does not change.

Internal and External Forces

An internal force cannot change the total momentum of a system.

It is important to define a system carefully. A force may be eityer internal or external depending on the system definition.

Conservation of Momentum in Two Dimensions

The total momentum of a system is the vector sum of the momenta of all the parts of the system.