1. Momentum and Impulse
8.01
W07D1 Fall 2006

2. Momentum and Impulse Obeys a conservation law
Simplifies complicated motions
Describes collisions
Basis of rocket propulsion & space travel

3. Quantity of Motion DEFINITION II Newton’s Principia
The quantity of motion is the measure of the same, arising from the velocity and quantity of matter conjointly.
The motion of the whole is the sum of the motions of all the parts; and therefore in a body double in quantity, with equal velocity, the motion is double; with twice the velocity, it is quadruple.

4. Momentum and Impulse: Single Particle
SI units
change in momentum
average force
impulse

5. Impulse Demo
To explain the demo and the example we need concepts of momentum and impulse
An explanation is easier if we also use the idea of center of mass

6. Jumping: Non-Constant Force
Plot of total external force vs. time for Andy jumping off the floor. Weight of Andy is 911 N.

7. Jumping: Impulse
Shaded area represents impulse of total force acting on Andy as he jumps off the floor

8. Newton’s Second Law
The change of motion is proportional to the motive force impresses, and is made in the direction of the right line in which that force is impressed,
Punctuation, minor formatting, conventional spelling is “Cartesian” with uppercase “C”.
When
then

9. Concept Question: Impulse and Change in Momentum
Identical constant forces push two identical objects A and B continuously from a starting line to a finish line. If A is initially at rest and B is initially moving to the right,
Object A has the larger change in momentum.
Object B has the larger change in momentum.
Both objects have the same change in momentum
Not enough information is given to decide.

10. Concept Question: Same Momentum, Different Masses
Suppose a ping-pong ball and a bowling ball are rolling toward you. Both have the same momentum, and you exert the same force to stop each. How do the distances needed to stop them compare?
It takes a shorter distance to stop the ping-pong ball.
Both take the same distance.
It takes a longer distance to stop the ping-pong ball.

11. Internal Force on a System of N Particles
The total internal force on the ith particle is sum of the interaction forces with all the other particles
The total internal force is the sum of the total internal force on each particle
Newton’s Third Law: internal forces cancel in pairs
So the total internal force is zero

12. Total Force on a System of N Particles is the External Force
The total force on a system of particles is the sum of the total external and total internal forces. Since the total internal force is zero

13. External Force and Momentum Change
The total momentum of a system of N particles is defined as the sum of the individual momenta of the particles
Total force changes the momentum of the system
Total force equals total external force
Newton’s Second and Third Laws for a system of particles: The total external force is equal to the change in momentum of the system

14. Position and Velocity of Center of Mass
Total mass
Position of center of mass
Velocity of center of mass

15. Translational Motion of the Center of Mass of Rigid Body
Momentum of system
System can be treated as point mass located at center of mass. External force accelerates center of mass
Impulse changes center of mass momentum

16. Jumping: Center of Mass Velocity
Plot of center of mass velocity vs. time starting from rest
Impulse for time interval
[ti, t] equals change in momentum of system.
Center of mass velocity at time t is then

17. Jumping: Center of Mass Velocity
When Andy leaves the ground, the impulse is
So the center of mass velocity is
What was the magnitude of the displacement of Andy’s center of mass after he left the floor?

18. What is the shape of the trajectory of the center of mass of this coin?
andrew.mcguckin.us/ art/coin_1280.jpg

19. CM moves as though all external forces on the system act on the CM
so the jumper’s cm follows a parabolic trajectory of a point moving in a uniform gravitational field

20. Fosbury Flop

21. Concept Question: Pushing Baseball Bat1 3 2
The greatest acceleration of the center of mass
will be produced by pushing with a force F at
Position 1
Position 2
Position 3
4. All the same