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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

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2.3 Bumper Cars

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2 3 bumper cars

2.3 Bumper Cars

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


2 3 bumper cars

Ideas for today

  • Momentum

  • Impulse

  • Conservation of momentum

  • Angular momentum

  • Angular impulse

  • Conservation of angular momentum


Observations about bumper cars

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

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


2 3 bumper cars

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 !


2 3 bumper cars

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


Exchanging momentum

Exchanging Momentum

  • Impulse

    • The only way to transfer momentum

    • Impulse = Force · Time

    • Impulse is a vector

  • Impulse = change in momentum

    = final momentum – initial momentum

    = mvf – mvi


2 3 bumper cars

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

Super/clay ball

(A)

or

(B)


2 3 bumper cars

  • 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

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.


Head on collisions

Bowling ball and golf ball

Head-On Collisions

Newton’s cradle

  • Cars exchange momentum via impulse

  • Total momentum remains unchanged

  • The least-massive car experiences largest change in velocity


2 3 bumper cars

Impulse(motion along a straight line)

Impulse= change in momentum or

= final momentum – initial momentum

= mvf – mvi

AND, we just saw:

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


2 3 bumper cars

F t = mvf – mvi = Impulse

Or

mvf – mvi

F =

t

  • Fast collision = big force!

  • Slow collision = small force


2 3 bumper cars

3000kg

2000kg

3000kg

2000kg

CLICKER QUESTION:Is momentum conserved in this collision?

Air track

Before collision

After collision

(A) Yes

(B) No


2 3 bumper cars

Elastic collision: no loss of kinetic energy

Inelastic collision:kinetic energy is lost

Momentum is always conserved!

(if no external forces)

This is an inelastic collision


Angular momentum

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

Train

Newton’s Third Lawof 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.


Exchanging angular momentum

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

Rotating stool

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


2 3 bumper cars

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.


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