2. Linear Momentum

3. Mathematical definition:
Linear Momentum
Mathematical definition:

4. Mathematical definition:
Linear Momentum
Mathematical definition:
Units:

5. What is the linear momentum of a jogger of mass 72 kg running at 4
What is the linear momentum of a jogger of mass 72 kg running at 4.5 m/s?

6. What is the linear momentum of a jogger of mass 72 kg running at 4
What is the linear momentum of a jogger of mass 72 kg running at 4.5 m/s?
What is the mass of a hockey puck sliding on the ice at 18.0 m/s if its momentum is 4.95 kg·m/s?

7. An open cart rolls along a frictionless track while it is raining
An open cart rolls along a frictionless track while it is raining. As it rolls, what happens to the speed of the cart as the rain collects in it? (Assume that the rain falls vertically into the cart.)
It speeds up.
It maintains constant speed.
It slows down.
It stops immediately.

8. Momentum of a system of masses:
Linear Momentum
Momentum of a system of masses:

9. At a city park a person throws some bread into a duck pond. Two 4
At a city park a person throws some bread into a duck pond. Two 4.00-kg ducks and a 9.0-kg goose paddle rapidly towards the bread. If the ducks swim at 1.10 m/s, and the goose swims at 1.30 m/s, as shown in the diagram, find the magnitude and direction of the momentum of the system of three birds.

10. A system of particles is known to have a total kinetic energy of zero.
What can you say about the total momentum of the system?
Momentum of the system is positive
Momentum of the system is negative
Momentum of the system is zero
You cannot say anything about the momentum of the system

11. A system of particles is known to have a total momentum of zero.
Does it necessarily follow that the total kinetic energy of the system is also zero?
Yes No

12. Linear Momentum and Newton’s Second Law

13. Linear Momentum and Newton’s Second Law

14. Linear Momentum and Newton’s Second Law
(assuming m is not changing)

15. Linear Momentum and Newton’s Second Law
(assuming m is not changing)
The rate of change of momentum is equal to the net external force

16. A net force of 200 N acts on a 100-kg boulder, and
a force of the same magnitude acts on a 130-g pebble.
How does the rate of change of the boulder’s momentum compare to the rate of change of the pebble’s momentum?
Greater than
Less than
Equal to

17. What do we call the change in kinetic energy?

18. What do we call the change in kinetic energy?

19. Likewise, we have a term for the change in linear momentum:

20. Likewise, we have a term for the change in linear momentum:
“Impulse”

21. Likewise, we have a term for the change in linear momentum:
“Impulse”
notice
This implies that impulse is force x time…

22. Likewise, we have a term for the change in linear momentum:
“Impulse”
notice
This implies that impulse is force x time…
… which can also be interpreted at area under a Force vs. time graph F F I t Dt

23. Likewise, we have a term for the change in linear momentum:
“Impulse”
notice
This implies that impulse is force x time…
… which can also be interpreted at area under a Force vs. time graph
But what if the force varies over time? F F I t Dt

26. When an athlete falls to the ground, a cushion can extend the time of impact, lowering the force exerted on him.
The impulse is the same as it would be if he landed on cement – the athlete’s momentum has to go to zero – but it’s done with a force that doesn’t hurt.

27. A 0. 145-kg baseball is thrown towards home plate at 95. 0 mph (42
A kg baseball is thrown towards home plate at 95.0 mph (42.47 m/s). (Assume it is initially traveling horizontally.)
Immediately after the hit the ball is traveling straight back towards the pitcher (again, horizontally) at 115 mph (51.41 m/s).
What was the average force of the bat on the ball?

28. What happens if the net external force is zero?

29. What happens if the net external force is zero?
Zero net external force means the momentum won’t change:

30. Linear Momentum is conserved
What happens if the net external force is zero?
Zero net external force means the momentum won’t change:
Linear Momentum is conserved
if there is no net external force