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Mr. Moe Mentum
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Mr. Moe Mentum
• We’ve talked about forces, but how do
they affect and relate to motion?
• If we remember Newton’s 2nd Law, the
net force = time rate change of
momentum
• momentum ()
– defined as mass of an object times its
velocity
• compare the momentum of a baby carriage and
bus
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Wild Impulses
• No, not those crazy things you regret later
• Impulse (J)
– a change in momentum
– Find force needed to stop bus
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Keep guns out of schools
• Newton’s third law states, “For every force
(reaction) there is an equal . . . “
• Consider a gun and bullet, right before
firing
– the bullet has a small mass and 0 velocity
• what is its momentum?
– the gun has a big(ger) mass and 0 velocity
• what is its momentum?
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Fire at will, Fire at will
• Which one’s Will?
• After firing, the bullet flies away, and the
gun kicks back in the other direction
• now the gun and the bullet have
momentum but the total momentum of
the system is not changed!
– one goes in the positive direction, the other
negative
• The bullet and the gun have equal and
opposite momentum
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Conservation, Part 1
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•
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Momentum doesn’t change
Momentum varies not
Momentum is not the stock market
Momentum is forever;
Only two things are certain – death and momentum!
Scientifically, we say:
• Momentum is conserved
– The total momentum of a closed system is
conserved
– closed system implies no external forces
– external force vs. internal force
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Momentum is useful?
• Conservation of momentum is a application of
Newton’s 3rd Law
• now we think it is a more fundamental law, and Newton’s
third law is a consequence of it!
– true of entire universe
• Can we use this in life?
– If I am on a space walk and my propellant systems
fail, how can I get back?
– What if I am floating in a ship and my engine
breaks down?
– In the middle of frictionless ice or on a skating
rink?
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Using Momentum
• For collisions and explosions
– we’ll explain later
• Ballistic pendulum
– find the velocity of a gun
• Softball Throw
– find how hard you can throw
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Types of Problems
• 3 basic types of problems
– explosions
• guns
– inelastic collisions
• things “stick”
– KE not conserved
– elastic collisions
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Location, Rotation
• Apply conservation to rotations
– the math gets tougher, but we can talk qualitatively
• Rotational Analogs
– mass
• now rotational inertia or moment of inertia
– how mass is distributed
» mass close together, small rotational inertia; vioce versa
– velocity
• now angular velocity
– how fast things spin
– force
• now torque
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Say Anything
• Restate conservation of momentum in
angular terms:
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Application
• Figure skater
– starts with arms out, then brings hands closer
• spin increases to conserve angular momentum
• how does she slow back down?
• Rotating Star
– as it dies, gravity causes it to collapse
• spin increases to conserve angular momentum
• Large rotational inertia * small spin rate = small
rotational inertia * large spin rate
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Precession
• Bicycle wheel
– when spinning, it doesn’t fall over; it rotates
• Spinning top
– the wobble is the precession
• Orbits too
– early proof of GR – measure of precession of
Mercury’s orbit (43 seconds)
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