1. Momentum Read Your Textbook: Introduction to Physical Science
Chapter 3.5
Chapter 4
Practice Homework Exercises

2. Motion Review Velocity = change in displacement = Dx Speed
change in time Dt
Acceleration = change in velocity = Dv How fast are you
change in time Dt getting faster.
Force = mass x acceleration = m Dv a = F/m Dt
A look at the two definitions of acceleration….

3. Force and Acceleration
F = m Dv = m a Dt
If a Force acts occurs over a short time,
a small acceleration results.
If a Force acts over a long time,
a large acceleration results.

4. Cannon Ball! F Dt = m Dv F = m Dv Dt
For the same Force (amount of powder), why is the speed of
a cannon ball greater when fired from a longer cannon barrel?
F = m Dv Dt

5. Interaction Time F Dt = m Dv
The longer cannon barrel gives the cannon ball a larger
impulse and therefore more momentum. The Force (F) is
allowed to act for a longer time Dt to build up velocity (Dv).

6. Impulse and Momentum acceleration = acceleration a = a
F = Dv F Dt = m Dv
m Dt
Impulse Momentum

7. Impulse and Momentum F = Dv F Dt = m Dv m Dt Impulse Momentum
If a change in velocity (momentum) occurs over a short time,
a large force must act.
If the change in velocity (momentum) occurs over an extended
time, a small force is acting.
Recall the Egg Toss Game
A Boxer Bobs and Weaves His Head
Bending Legs Upon a Parachute Landing

8. Conservation of Momentum
Momentum is a conserved quantity, that is, for any isolated
system, the total momentum remains unchanged.
Momentum = mass x velocity P = m v

9. Conservation of Momentum
Momentum is a conserved quantity, that is, for any isolated
system, the total momentum remains unchanged.
Momentum = mass x velocity P = m v
Consider the following collision:
Before After v M m V

10. Conservation of Momentum
Momentum is a conserved quantity, that is, for any isolated
system, the total momentum remains unchanged.
Momentum = mass x velocity P = m v
Consider the following collision:
Before After v V’ M m m M v’ V

11. Conservation of Momentum
Momentum is a conserved quantity, that is, for any isolated
system, the total momentum remains unchanged.
Momentum = mass x velocity P = m v
Consider the following collision:
Before After
Total Momentum
MV + mv = total momentum = MV’ + mv’ v V’ M m m M v’ V

12. Ice Ball Toss v M m Total Momentum Before: M V + m v
60 kg ( 0 km/hr) + 20 kg (10 km/hr) = 200

13. Ice Toss Momentum After (must be identical to momentum before) = 200
= (M+m) v’
200 = (M+m) v’
200 = (60+20) v’
v’ = 200/80 = 2.5 km/hr

14. Conservation of Momentum
What is the total momentum of the debris from a firecracker?
Before After
M V = 0 = total momentum before
Total Momentum After = m1v1 + m2v2 + m3v3 + … m2 m1 m3 m4

15. Conservation of Momentum
What is the total momentum of the debris from a firecracker?
Before After
M V = 0 = total momentum before
Total Momentum After = m1v1 + m2v2 + m3v3 + …
= 0 m2 m1 m3 m4

16. Rifle Shot
Let mbullet = 0.3 kg, Mrifle = 5 kg, and vbullet = 370 m/s
mbulletvbullet + MrifleVrifle = 0.3 kg (370 m/s) + 5kgVrifle
0 = 0.3 kg (370 m/s) + 5kgVrifle

17. Rifle Shot If momentum is conserved, why doesn’t a rifle kill you upon
recoil after firing a bullet?
Before: mbulletvbullet + MrifleVrifle = 0

18. Rifle Shot If momentum is conserved, why doesn’t a rifle kill you upon
recoil after firing a bullet?
Before: mbulletvbullet + MrifleVrifle = 0
After: = 0
Let mbullet = 0.3 kg, Mrifle = 5 kg, and vbullet = 370 m/s

19. Rifle Shot
Let mbullet = 0.3 kg, Mrifle = 5 kg, and vbullet = 370 m/s
mbulletvbullet + MrifleVrifle = 0.3 kg (370 m/s) + 5kgVrifle
0 = 0.3 kg (370 m/s) + 5kgVrifle
-0.3(370) = 5 kg Vrifle
Vrifle = - 0.3(370)/5 = m/s

20. Mriflevrecoil = mbulletVbullet
Rifle Shot
Let mbullet = 0.3 kg, Mrifle = 5 kg, and vbullet = 370 m/s
mbulletvbullet + MrifleVrifle = 0.3 kg (370 m/s) + 5kgVrifle
0 = 0.3 kg (370 m/s) + 5kgVrifle
-0.3(370) = 5 kg Vrifle
Vrifle = - 0.3(370)/5 = m/s
Shoulder aches, BUT your alive!
Mriflevrecoil = mbulletVbullet

21. Now you try:
What is the velocity of a bullet (m = 0.15 kg) after being fired from a 10 kg rifle (NOTE: rifle recoils with a velocity of 3 m/s).
A. 30 m/s
B m/s
C. 200 m/s
D. 310 m/s
E. none of these
mbulletvbullet + MrifleVrifle = kg (vbullet) + 10kg (3 m/s)
0 = kg (vbullet) + 30 kg m/s
-30 kg m/s = 0.15 kg vbullet
vbullet = - 30 kg m/s /(0.15 kg) = m/s

22. Train Link An train engine runs into a stationary box car
weighing 4x more than itself to link up. If the engine
was traveling 10 mph before link up, how fast does
the train move after?

23. Train Link An train engine runs into a stationary box car
weighing 4x more than itself to link up. If the engine
was traveling 10 mph before link up, how fast does
the train move after?
MOMENTUM BEFORE = MOMENTUM AFTER
MVBC = (M + 4M) VAC

24. Train Link An train engine runs into a stationary box car
weighing 4x more than itself to link up. If the engine
was traveling 10 mph before link up, how fast does
the train move after?
MOMENTUM BEFORE = MOMENTUM AFTER
MVBC = (M + 4M) VAC
M(10) = (5M) VAC
10 = 5 VAC
2 = VAC

25. Angular Momentum L Angular Momentum: A combination of... m Mass
v Speed of Rotation
r Mass Position (with respect to rotational axis)
L = m v r
Conservation Examples:
Spins of Dancers or Ice Skaters
Those Funky Coin Vortexes in Stores
Tops and Gyroscopes
Riding a Bicycle

26. Precession and the Earth
1 complete cycle takes 26,000 years

27. Orbit Application Angular Momentum L,
is the product of a planet's mass (m),
orbital velocity (v)
and distance from the Sun (R).
The formula is simple: L = m v R,
where R = a function of e the eccentricity.

28. Faster, Closer
Conservation of Angular Momentum: L = L
m V r m v R

29. Summary Impulse and Momentum Conservation of Momentum Angular Momentum
F Dt = m Dv
Conservation of Momentum
Total Momentum (P = M V)
Angular Momentum
L = m v r