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# circular motion and angular momentum

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Question #1
A grindstone of radius 4.0m is initially spinning with an angular speed of 8.0 rad/s. The angular speed is then increased to 10 rad/s over the next 4.0 seconds. Assume that the angular acceleration is constant.
A. What is the average angular speed of the grindstone?
B. What is the magnitude of the angular acceleration of the grindstone?
C. Through how many revolutions does the grindstone turn during the 4.0-second interval?

Question #2.
A wheel of the radius 0.5m rotates with a constant angular speed about an axis perpendicular to its center. A point on the wheel that is 0.2m from the center has a tangential speed of 2m/s.
A. Determine the Angular speed of the wheel?
B. Determine the tangential speed of a point 0.4m from the center of the wheel?
C. Determine the tangential acceleration of the point that is 0.2m from the center?

Question #3
An 80-kg man balances the boy on a teeter-totter as shown. (Note: Ignore the weight of the board)
A. What is the approximate mass of the boy?
B. What approximately, is the magnitude of the downward force exerted on the fulcrum?

Question #4
A spinning star begins to collapse under its own gravitational pull. Which one of the following occurs as the star becomes smaller? Explain?
A. Its angular velocity decreases.
B. Its angular momentum increases.
C. Its angular velocity remains constant.
D. Its angular momentum remains constant.
E. Both its angular momentum and its angular velocity remain constant.

Question #5
A spinning skater draws in her outstretched arms thereby reducing her moment of inertia by a factor of 2. Determine the ratio of her final kinetic energy to her initial kinetic energy?

Question #6
Two skaters, each of a mass 40kg, approach each other along parallel paths that are separated by a distance of 2m. Both skaters have a speed of 10m/s. The first skater carries a 2-m pole that may be considered massless. As he passes the pole, the second skater catches hold of the end. The two skaters then go around in a circle about the center of the pole.
A. What is the angular speed of the skaters after they have linked together?
B. What is their combined angular momentum about the center of the pole?

Question #7
A 2.0-kg hoop rolls without slipping on a horizontal surface so that its center proceeds to the right with a constant linear speed of 6.0m/s.
A. Which one of the following statements is true concerning the angular momentum of this hoop?
#1. It points into the paper.
#2. It points out of the paper.
#3. It points to the left.
#4. It points to the right.
#5. It varies from point to point on the hoop.

B. What is the total kinetic energy of the hoop?

Question #8
During the spin-dry cycle of a washing machine, the motor slows from 95 rad/s to 30 rad/s while the turning the drum through an angle of 402 radians. What is the magnitude of the angular acceleration of the motor?

See attached file for full problem description.