Chapter C14 Conservation of angular momentum Problem S.2 Due Wednesday

Problems due Wednesday Problems S.2 Due Wednesday Test is Monday Many of the answers to the practice test are on the physics webpage. It is possible that some errors exist in the answers so don’t spend a great deal of time, ask about them in class.

Definitions Twirl is the interaction (force) that tends to make an object rotate. Torque is a vector quantity that measures the tendency of an object to rotate. A torque causes a change in the angular momentum

Torque ( ) Where a force F is applied at a distance r from the center of rotation.

The conservation laws The fact that energy is conserved implies that the laws of physics do not change with time The fact that momentum is conserved implies that the laws of physics are the same in all space The conservation of angular momentum implies that the laws of physics are the same in any direction.

Noether’s Theorem Conservation of energy –Means physical laws do not change in time Conservation of linear momentum –Means physical laws are the same anyplace in the Universe. Conservation of angular momentum –Means physical laws are the same regardless of how you are oriented Same in all directions. The most important idea this year

Applications of conservation of angular momentum A 40 kg boy is on the outside of a merry-go- round of radius 4 m (spinning disk) that is spinning 6 rev/min. What happen if walks toward the center until he is half way to the center at r = 2 m? Case 1, merry-go-round has no mass.

Principle Angular momentum is conserved The angular momentum when the boy is on the outside of the disk is the same as the angular momentum when he is half way toward the center. L 0 =L f I 0 ω 0 =I f ω f r o mv o = r f mv f When the boy walks toward the center the disk spins faster. If he walks halfway to the center the wheel spins twice as fast. What is the direction of his angular momentum? What would happen if he walked all the way to the center?

Applications of conservation of angular momentum A 40 kg boy is on the outside of a merry-go- round of radius 4 m (spinning disk) that is spinning 6 rev/min. What happen if walks toward the center until he is at r = 2m? Case 2, merry-go-round has a mass of 80 kg.

Write the principle The angular momentum of the boy and of the disk before he moves is equal to the angular momentum of the boy and the disk after he moves. Write the equations for the boy on the outside of the disk. Mass of boy = m b, velocity = v 1 Radius = r 1

Write the equations for after he moves. Remember that r 1 =2r 2 Solve the problem to find the final velocity of the disk in this case.

A comet is going 100 m/s when it is 100 au from the sun, how fast is it going when it is.3 au from the sun? Principle Angular momentum is conserved The angular momentum of the comet is the same when it is far from the sun as when it is close. mv 1 r 1 =mv 2 r 2 v 2 =33,333 m/s

Problems due Wednesday Problems S.2 Due Wednesday