2.3 Bumper Cars Or: why you must always wear your seat belt, and pull it tight!

Ideas for today Momentum Impulse Conservation of momentum Angular momentum Angular impulse Conservation of angular momentum

Observations about “Bumper Cars” Moving or spinning cars tend to keep doing so It takes time to change a car’s motion Impacts change velocities & angular velocities Cars often seem to exchange their motions Heavily loaded cars are hardest to redirect Heavily loaded cars pack the most wallop

Momentum Anything moving has momentum Momentum –A conserved quantity (can’t create or destroy) in the absence of external forces –A vector Momentum = Mass x Velocity

The fire engine is 13 times more massive than the car, so will have 13 times more momentum at the same speed. It also requires 13 times more impulse to stop it !

While the cars passing (see the taillights in the long-time exposure) have momentum, this massive building has none.

Exchanging Momentum Impulse –The only way to transfer momentum –Impulse = Force · Time –Impulse is a vector ImpulseImpulse = change in momentum = final momentum – initial momentum = mv f – mv i

CLICKER QUESTION: Which person has the greater impulse exerted on his shield? (A) or (B) Super/clay ball

The conservation of linear momentum states that, in the absence of net external forces, the total vector momentum before a collision is the same as the total vector momentum after the collision. Because of Newton’s third law: An impulse of one object on a second is accompanied by an equal but oppositely directed impulse of the second on the first. Air track

Head-On Collisions Cars exchange momentum via impulse Total momentum remains unchanged The least-massive car experiences largest change in velocity Bowling ball and golf ball Newton’s cradle

Impulse Impulse = change in momentum or = final momentum – initial momentum = mv f – mv i AND, we just saw: Impulse Impulse = Force applied times the time the force is applied = F t Impulse Impulse (motion along a straight line)

F t = mv f – mv i = Impulse Or mv f – mv i F = t Fast collision = big force! Slow collision = small force

CLICKER QUESTION: CLICKER QUESTION: Is momentum conserved in this collision? Before collision After collision 3000kg 2000kg (A) Yes (B) No Air track

Elastic collision Elastic collision: no loss of kinetic energy Inelastic collision: Inelastic collision: kinetic energy is lost Momentum is always conserved! (if no external forces) This is an inelastic collision

Angular Momentum A spinning car carries angular momentum Angular momentum –A conserved quantity (can’t create or destroy) –A directed (vector) quantity Angular momentum = Rotational mass x Angular velocity

Newton’s Third Law of Rotational Motion For every torque that one object exerts on a second object, there is an equal but oppositely directed torque that the second object exerts on the first object. Angular momentum is conserved in the absence of external torques. Train

Exchanging Angular Momentum Angular Impulse –The only way to transfer angular momentum –Angular impulse = Torque · Time –Angular impulse is a vector Because of Newton’s third law of rotation: An angular impulse of one object on a second is accompanied by an equal but oppositely directed angular impulse of the second on the first.

Changing Rotational Mass Mass can’t change, so the only way an object’s velocity can change is if its momentum changes Rotational mass can change, so an object that changes shape can change its angular velocity without changing its angular momentum Rotating stool

In the air, motorcycle riders control their bikes by revving up their motors to spin the rear tire faster, or by putting on the brakes to slow the tire. This changes the angular momentum of their system internally, giving them control of the angle at which they come down.