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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.