1. Momentum & Impulse
Topic 2.2

2. Momentum What makes an object hard to stop?
Is it harder to stop a bullet, or a truck travelling along the highway?
What makes each object hard to stop?

3. Momentum (kg.m.s-1) = Mass (kg) x Velocity (m.s-1)
Momentum is a useful quantity to consider when thinking about "unstoppability". It is also useful when considering collisions and explosions. It is defined as
Momentum (kg.m.s-1) = Mass (kg) x Velocity (m.s-1)
p = mv

4. An easy example
A truck has a mass of kg and a velocity of 3 m.s-1. What is its momentum?
Momentum = Mass x velocity
= x 3
= kg.m.s-1.

5. Linear Momentum
The momentum p of a body of constant mass m moving with velocity v is, by definition mv
p = mv
It is a vector quantity
Its units are kg m s-1 or Ns
It is the property of a moving body.

6. Conservation of momentum
In a collision between two objects, momentum is conserved (total momentum stays the same)
In an isolated system (no outside forces), momentum remains constant
isolated system = translational equilibrium
We can use this to calculate what happens after a collision (and in fact during an “explosion”).
Momentum is not energy!

7. Deriving This Law
To derive this law we apply Newton´s 2nd law to each body and Newton´s 3rd law to the system
i.e. Imagine 2 bodies A and B interacting
mass of mA and mB
A has a velocity change of uA to vA and
B has a velocity change of uB to vB during the time of the interaction t

8. Then the force on A given by Newton 2 is
FA = mAvA – mAuA t
And the force on B is
FB = mBvB – mBuB t
But Newton 3 says that these 2 forces are equal in magnitude and opposite in direction

9. Therefore
mAvA – mAuA = - (mBvB – mBuB) t t
mAvA – mAuA = mBuB – mBvB
Rearranging gives:
mAuA + mBuB = mAvA + mBvB
Total Momentum before =
Total Momentum after

10. Momentum is a vector
Momentum is a vector, so if velocities are in opposite directions we must take this into account in our calculations

11. Newton´s Second Law - Revisited
F = ma F = m v - m u t t
F = mv – mu F =p t t
The rate of change of momentum of a body is proportional to the resultant force and occurs in the direction of the force.

12. Impulse Where have you heard this term? Some Examples:
I bought that from the internet on impulse after seeing the commercial on TV
I got into a fight on impulse after being called a name

13. Impulse F = p F = mv – mu t t Ft = mv – mu = p
This quantity Ft is called the impulse of the force on the body
It is a vector quantity
Its units are kg m s-1or Ns

14. Impulse = Change in momentum
Ft = mv – mu = p
The quantity Ft is called the impulse, and
mv – mu is the change in momentum
(v = final velocity and u = initial velocity)
Impulse = Change in momentum

15. Units or [kg.m.s-2]x[s] = [kg.m.s-1] (mv – mu)
Impulse is measured in N.s (Ft)
or [kg.m.s-2]x[s] = [kg.m.s-1]
(mv – mu)

16. Impulse
Note: For a ball (mass m) bouncing off a wall, don’t forget the initial and final velocity are in different directions, so you will have to make one of them negative.
In this case mv – mu = 5m – (-3m) = 8m
5 m/s
-3 m/s

17. Another example
A tennis ball (0.3 kg) hits a racquet at 3 m/s and rebounds in the opposite direction at 6 m/s. What impulse is given to the ball?

18. Another example
A tennis ball (0.3 kg) hits a racquet at 3 m/s and rebounds in the opposite direction at 6 m/s. What impulse is given to the ball?
3 m/s
-6 m/s

19. Another example = 0.3x-6 – 0.3x3 = -2.7kg.m.s-1 Impulse = mv – mu =
A tennis ball (0.3 kg) hits a racquet at 3 m/s and rebounds in the opposite direction at 6 m/s. What impulse is given to the ball?
Impulse = mv – mu =
= 0.3x-6 – 0.3x3
= -2.7kg.m.s-1
3 m/s
-6 m/s