MOMENTUM!
Momentum Defined: p = m v
 p = momentum vector
 m = mass
 v = velocity vector
Momentum Facts
 Linear Momentum: p = m v
 Momentum is a vector quantity!
 Velocity and momentum vectors point in the same direction.
 SI unit for momentum: kg · m /s (no special name).
 Momentum is a conserved quantity (this will be proven later).
 A net force is required to change a body’s momentum.
 Momentum is directly proportional to both mass and speed.
 Something big and slow could have the same momentum as
something small and fast.
Momentum Examples
 Equivalent Momenta - The train, bus, and car all have different masses and speeds, but their momenta
are the same in magnitude. The massive train has a slow speed; the low-mass car has a great speed; and
the bus has moderate mass and speed. Note: We can only say that the magnitudes of their momenta are
equal since they’re aren’t moving in the same direction.
 The difficulty in bringing each vehicle to rest--in terms of a combination of the force and time required-would be the same, since they each have the same momentum.
Newton’s 2nd Law in terms of momentum
 p = mv, F = Δp/Δt
Practice
1) Calculate the momentum of a 110kg rugby player running the 100m in 15s.
2) Calculate the force that the rugby player in the previous example imparts on your body if, during a
tackle you halve his speed in the time of 0.2s
Impulse
 When two object collide, their velocities change and since momentum is a function of an object’s
velocity, the momentum changes. This change in momentum is called impulse(I).
 Same unit as momentum, kgm/s
 Can be defined as a force times a time.
 Units can also be Ns
 I = Δp
 I = p2 – p1
 I = mv – mu
 I = mΔv




F = ma
F = Δp/Δt
F = I/ Δt since I = Δp
I = FΔt
Impulse Practice
• A fielder catches a 0.4kg cricket ball travelling at a velocity of 20m/s and brings it to a stop. Calculate
a)The impulse(change in momentum) of the cricket ball
b)The force on the fielder’s hand if he stops the ball with a rigid arm, where the time for the ball to come to rest
is 0.02s
c)The force on the fielder’s hand if he brings the ball to rest more gradually, say in a time of 0.5s
Conservation of Momentum in 1-D
Whenever two objects collide (or when they exert forces on each other without colliding, such as gravity)
momentum of the system (both objects together) is conserved. This mean the total momentum of the objects is
the same before and after the collision.
• Directions after a collision
On the last slide the boxes were drawn going in the opposite direction after colliding. This isn’t always the
case. For example, when a bat hits a ball, the ball changes direction, but the bat doesn’t. It doesn’t really
matter, though, which way we draw the velocity vectors in “after” picture. If we solved the conservation of
momentum equation (red box) for vb and got a negative answer, it would mean that m2 was still moving to the
left after the collision. As long as we interpret our answers correctly, it matters not how the velocity vectors are
drawn.
Sample Problem 1
1. A rifle fires a bullet into a giant slab of butter on a frictionless surface. The bullet penetrates the butter,
but while passing through it, the bullet pushes the butter to the left, and the butter pushes the bullet just
as hard to the right, slowing the bullet down. If the butter skids off at 4 cm/s after the bullet passes
through it, what is the final speed of the bullet?
(The mass of the rifle matters not.)
Sample Problem 2
2) Same as the last problem except this time it’s a block of wood rather than butter, and the bullet does not
pass all the way through it. How fast do they move together after impact?