1. The Physics of Bumper Car Collisions
and Spinning Tops & Gyroscopes

2. Bumper Car Observations
Moving or Spinning Cars tend to keep doing so.
Impacts change car linear and angular velocities.
After colliding, cars exchange velocities.
Heavily-loaded cars seem less affected,
Lightly-loaded cars bounce away easily
WHY ?

3. Suppose there were no collisions, no friction….
……Then car would simply go on and on….: m
Car carries ‘momentum’ – a ‘ quantity of motion’ that is conserved.
p = linear momentum = (mass)(velocity) = mv a vector
Let there now be a collision against a second car: m
p1 = m1v1
p2 = 0
We expect a transfer or an exchange of momentum

4. Impulse I – method of transferring momentum = (Force)(t)
p1 = m1v1 m m
p2 = 0
- F F
In contact for time t m m
p2’’ = m2v2’
P1’ = m1v1’ m m
Because of Newton’s 3rd law,
Impulse of first object on the second is accompanied by an
equal and oppositely directed impulse from the second on the first.
Impulse I = change in momentum….. or Ft = p

5. If no net external forces exist , Total momentum of the
system is conserved,
In collisions, the least massive object suffers the greatest
change in velocity.
Example: Before Collision
V= 0 m/s
V=1 m/s
10 kg
1kg
10 kg
1kg
V=0.9 m/s
V= 10 m/s
After Collision:
What was the impulse felt by the little car if collision happened in 1 second ?

6. Everyday Application: Automobile bumpers
Why are bumpers made of rubber, and not something stiff like
metal ?
Rubber is more elastic than metal. For the same impulse I= Ft
felt, the longer impulse time t leads to a smaller impact force F
What happens if the car is not struck head-on but clipped
on its back or front ?
Car spins after collision

7. Angular Momentum L – the quantity of spinning motion
Spinning cars have angular momentum
a conserved, vector quantity that gives you a measure
of the spinning motion
transferred/exchanged through angular Impulse
If no net torque on a system, L is conserved.
Analogy between Linear and Angular Momentum
Linear Angular
p, linear momentum L, angular momentum
P = mv L = I 
Ft = p Tt = L , where T = torque

8. Tt = L Applying a torque on a system for a period
of time changes its Angular Momentum
(To spin a top faster, you need to twist it harder…..)
Other Applications: Tops and Gyroscopes
L = I
L = I

9. Why do Spinning wheels precess (and not fall) ? F Tt = L , L1
ceiling F
Tt = L , L1
where T = r x mg r L L1
Since L is in the same direction as
the torque T, the spin precesses like
a top Instead of falling. mg

10. Slow rotation Fast Rotation
Can a change in Moment of Inertia result in faster spins ?
Arms extended vs Arms Withdrawn
L1 = L2
I11 = I11
Slow rotation Fast Rotation
By drawing arms inwards, the spinning skater reduces her
moment of inertia I. If angular momentum L is conserved,
This results in a larger , thus resulting in a faster spin.