1. Chapter 7
Impulse and Momentum

2. 1) Definition
p = mv

3. 2) Impulse For a constant force, From the 2nd law,
If the force is not constant, use the average force

4. 7) Conservation of momentum in 2d
If initial conditions are known, this
gives 2 equations, with 4 unknowns,
so more information is needed.
v1’
v2’

5. 7) Conservation of momentum in 2d
a) Inelastic collision: p1’ = p2’ = p’ reduces unknowns to px’ and py’
Example: Find v’ if m1 = 1450 kg, m2 = 1750 kg, v1 = 11.5 m/s, v2 = 15.5 m/ss
• conservation of x momentum m1 m2 v1 v2 v’ x y 
• conservation of y momentum

6. 7) Conservation of momentum in 2d
b) Elastic collision: Energy conservation adds 3rd equation:
The last condition is determined by the shape & location of impact:
e.g. F
For a billiard ball collision, the angle of the object ball is
determined by the line through the centres at the point of contact.

7. 7) Conservation of momentum in 2d
b) Elastic collision: Energy conservation adds 3rd equation:
Conservation of momentum v1
v2’
v1’ F 1
Example: Cue ball angle:
• identical masses
• elastic collision
• m2 initially at rest
2?
Conservation of energy
v2’
v1’ v1
Therefore, by Pythagoras

8. 8) Centre of Mass Acceleration and force:
The centre-of-mass of a system of particles (or 3d object) reacts to the sum of the forces like a point particle with a mass equal to the total mass of the particles.
If the total force is zero, the centre-of-mass does not
accelerate. (If there are no external forces, the internal
forces sum to zero by the 3rd law.)

9. 8) Centre of Mass b) Momentum and velocity Since a = v/t,
But, since vCM = 0 if v1 = 0 and v2 = 0, this becomess
The numerator represents the total momentum, which is conserved
in the absence of external forces, so again, the centre-of-mass
velocity is constant. Note that the CM momentum is simply equal
to the total momentum:

10. 8) Centre of Mass c) Position of the centre of mass
Since v = x/t, the above gives
If 2 particles coincide, they also coincide with the CM, so
In one dimension,
For m1 = 5.0 kg, m2 = 12 kg, x1 = 2.0 m, and x2 = 6.0 m,
xCM = 4.8 m