1. A pulley of radius 0.3 m is rotating counter-clockwise and is pulling a weight upward. The weight slows the spinning pulley so that it comes to rest. The angular acceleration is -2.10 R/s^2
a. If the pulley's initial angular speed is 5.4 R/s, how many seconds does it take for the pulley to come to rest?
b. Through what angle in radians does the pulley turn during this time?
c. What was the initial upward speed in m/s of the weight?
2. Two children Jason and Betsy, ride on the same merry-go-round. Jason is a distance R from the axis of rotation; Betsy is a distance 2R from the axis.
a. The angular speed of Jason is (<, >, =) the angular speed of Betsy.
b. Choose the best explanation from among the following:
I. The period is grater for Jason because he moves more slowly than Betsy.
II. The period is greater for Betsy since she must go around the circle at a larger circumference.
III. It takes the same amount of time for the merry-to-round to complete one revolution for all points on the merry-go-round.
c. What is the ratio of Jason's angular speed to Betsy's angular speed?
d. What is the ratio of Jason's linear speed to Betsy's angular speed?
e. What is the ratio of Jason's centripetal acceleration to Betsy's centripetal acceleration?
3. Two football players interact on the field. One moving toward the right is carrying the ball and wants to cross the goal line. The other player moving toward the left tackles the ball carrier and holds on to the player. If the player moving toward the right has a mass of 95 kg and is moving at 3.75 m/s, and the player moving toward the left has a mass of 111 kg and is moving at 4.1 m/s,
a. What is the total momentum of the two players before they collide (vectors to the right should be designated as positive)?
b. What is the velocity of the pair immediately after the collision?
c. Is the pair moving toward the right or the left?
d. What is the total kinetic energy of the two players before the collision in Joules?
e. What is the total kinetic energy of the two players after the collision in Joules?
4. A car engine is initially rotating at 200 rad/s. It is then turned off and takes 3.0 s to come to a complete stop. Assuming that the acceleration is constant, what is the angular acceleration of the engine in R/s^2