2.3 Bumper 2.3 Bumper CarsCars

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

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

Observations about “Bumper Observations about “Bumper Cars”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

MomentumMomentum• Anything moving has momentum• Momentum

– A conserved quantity (can’t create or destroy) in the absence of external forces

– A vector

Momentum = Mass Momentum = Mass x x VelocityVelocity

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

= mvf – mvi

CLICKER QUESTION:Which person has the greater impulse exerted on his shield?

(A)

or

(B)

Super/clay ball 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 Air track

Head-On CollisionsHead-On Collisions• Cars exchange momentum via impulse• Total momentum remains unchanged• The least-massive car experiences largest

change in velocity

Bowling ball and golf Bowling ball and golf ballball

Newton’s Newton’s cradle cradle

ImpulseImpulse = change in momentum or

= final momentum – initial momentum

= mvf – mvi

AND, we just saw:

ImpulseImpulse = Force applied times the time the force is applied = F t

ImpulseImpulse (motion along a straight line)

F t = mvf – mvi = Impulse

Or

mvf – mviF =t

• Fast collision = big force!• Slow collision = small force

CLICKER QUESTION:CLICKER QUESTION:Is momentum conserved in this collision?

Before collision

After collision

3000kg

3000kg

2000kg

2000kg

(A) Yes

(B) No

Air track Air track

Elastic collisionElastic 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 MomentumAngular Momentum• A spinning car carries angular momentum• Angular momentum

– A conserved quantity (can’t create or destroy)

– A directed (vector) quantity

Angular momentum = Angular momentum = Rotational mass Rotational mass x Angular velocityx Angular velocity

Newton’s Third LawNewton’s Third Lawof Rotational Motionof 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.

TrainTrain

Exchanging Angular Exchanging Angular MomentumMomentum• 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 MassChanging 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 Rotating stool 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.