Transcript Bumper Cars and Spinning Tops

The Physics of Bumper Car Collisions
and Spinning Tops & Gyroscopes
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 ?
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:
p2 = 0
p1 = m1v1
m
m
We expect a transfer or an exchange of momentum
Impulse I – method of transferring momentum = (Force)(t)
p2 = 0
p1 = m1v1
m
m
-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
• 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=1 m/s
10 kg
V= 0 m/s
1kg
After Collision:
V=0.9 m/s
10 kg
V= 10 m/s
1kg
What was the impulse felt by the little car if collision happened in 1 second ?
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
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
p, linear momentum
P = mv
Ft = p
Angular
L, angular momentum
L=I
Tt = L , where T = torque
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
ceiling
Why do Spinning wheels
precess (and not fall) ?
F
L1
L
Tt = L ,
where T = r x mg
r
L1
Since L is in the same direction as
the torque T, the spin precesses like
a top Instead of falling.
mg
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.