1. Momentum – The Basics
Momentum is mass in motion (or inertia in motion)
Momentum is abbreviated as the letter p!
Momentum is mass x velocity (p = mv)
Both mass and velocity are needed to have momentum
The units of Momentum are kg•m/s or N•s

2. Historical Connections
Newton’s 2nd Law (F = ma) was originally written in terms of momentum where:
The familiar form is derived by writing the Law as:
ΣF = Δp Δt Δv Δt
ΣF =
mvF-mvI
= m
ΣF = Δp Δt
= ma Δv Δt
= a
since
We can conclude:

3. Impulse momentum changes due to a force force x time = impulse
impulse is the change in momentum
F Δt = Δ (m v) = m Δv (most of the time) Δv Δt
F = m
Force (N)
time (s)

4. Impulse at work Increase momentum of ball Decrease momentum in a crash
high force (swing hard)
long time (follow through on swing)
Decrease momentum in a crash
long time during crash
reduces force for same momentum
F Δt = Δ(m v)

5. Bouncing Bouncing causes greater change in momentum
Greater impulse to reverse direction than just to stop it

6. Linear Momentum Velocity in a straight line One dimensional
along x or y axis
Two dimensional
some components of velocity in both x and y axis

7. The System A system is a collection of objects.
A system is closed when objects do not enter or leave it. (Similar to a class where students cannot add or drop.)
Isolated systems cannot have any external forces acting upon them.
A system that is both closed and isolated is needed to study momentum changes in collisions

8. Conservation of Momentum
The Law: In the absence of an external force, the momentum of a system remains unchanged.
Internal forces do not change total momentum.
Momentum is a vector (has direction).

9. Collisions
net momentum before collision equals net momentum after collision.
Elastic collision
no permanent deformation
no heat
objects separate after collision
Inelastic collision
objects become distorted
heat
objects stick together

10. Equations for Collisions
Elastic Collision (bouncy, objects separate at beginning and end)
m1v1i + m2v2i = m1v1f + m2v2f
Inelastic Collision (sticky)
m1v1i + m2v2i = (m1 + m2)vf
If an object splits into two pieces…the explosion!
(m1 + m2)vi = m1v1f + m2v2f

11. Example Problem 1
A 5.0 kg bowling ball with a velocity of 0.50 m/s rolls into a 6.5 kg bowling ball at rest. After the collision, the second ball travels at 0.43 m/s. What is the velocity of the first ball after the collision?

12. Example Problem 2
A 2500-kg van traveling at 14 m/s runs into the back of a 910-kg car at rest. The vehicles stick together after the collision. What is the final velocity?

13. Momentum is a vector
momentum vectors of the objects before the collision equal the momentum vectors of the objects after the collision