1 Mr. Moe Mentum

2 We’ve talked about forces, but how do they affect and relate to motion? If we remember Newton’s 2 nd 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

3 Wild Impulses No, not those crazy things you regret later Impulse (J) –a change in momentum –Find force needed to stop bus

4 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?

5 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

6 Conservation, Part 1 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

7 Momentum is useful? Conservation of momentum is a application of Newton’s 3 rd 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?

8 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

9 Types of Problems 3 basic types of problems –explosions guns –inelastic collisions things “stick” –KE not conserved –elastic collisions

10 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

11 Say Anything Restate conservation of momentum in angular terms:

12 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

13 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)