The Physics of Bumper Car Collisions and Spinning Tops & Gyroscopes

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….: p2 = 0 p1 = m1v1 m m 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: We expect a transfer or an exchange of momentum

4. m m m m m m Impulse I – method of transferring momentum = (Force)(t) p2 = 0 p1 = m1v1 - F F In contact for time t p2’’= m2v2’ P1’ = m1v1’ 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. After Collision: V= 10 m/s V=0.9 m/s 10 kg 1kg • 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 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 = mvL = 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) ? 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. 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.