1. 12.2 Force is the Rate of Change of Momentum

2. Chapter 12 Objectives
Calculate the linear momentum of a moving object given the mass and velocity.
Describe the relationship between linear momentum and force.
Solve a one-dimensional elastic collision problem using momentum conservation.
Describe the properties of angular momentum in a system—for instance, a bicycle.
Calculate the angular momentum of a rotating object with a simple shape. 2

3. Chapter Vocabulary angular momentum collision law of conservation of
elastic collision
gyroscope
impulse
inelastic collision
linear momentum

4. 12.2 Force is the Rate of Change of Momentum
Investigation Key Question:
How are force and momentum related?

5. 12.2 Force is the Rate of Change of Momentum
Momentum changes when a net force is applied.
The inverse is also true:
If momentum changes, forces are created.
If momentum changes quickly, large forces are involved.

6. 12.2 Force and Momentum Change
The relationship between force and motion follows directly from Newton's second law.
Force (N)
F = D p
D t
Change in momentum
(kg m/sec)
Change in time (sec)

7. Calculating force You are asked for force exerted on rocket.
Starting at rest, an 1,800 kg rocket takes off, ejecting 100 kg of fuel per second out of its nozzle at a speed of 2,500 m/sec. Calculate the force on the rocket from the change in momentum of the fuel.
You are asked for force exerted on rocket.
You are given rate of fuel ejection and speed of rocket
Use F = Δ ÷Δt
Solve: Δ = (100 kg) (-25,000 kg m/s) ÷ (1s) = - 25,000 N
The fuel exerts and equal and opposite force on rocket of +25,000 N.

8. 12.2 Impulse
The product of a force and the time the force acts is called the impulse.
Impulse is a way to measure a change in momentum because it is not always possible to calculate force and time individually since collisions happen so fast.

9. 12.2 Force and Momentum Change
To find the impulse, you rearrange the momentum form of the second law.
Impulse (N•sec)
F D t = D p
Change in
momentum
(kg•m/sec)
Impulse can be expressed in kg•m/sec (momentum units) or in N•sec.