(With Solutions)

1. A car accelerates uniformly from rest and reaches a Speed of 22.0 m/s in 9.00 s. If the radius of a tire is 29 cm, find the number of revolutions the tire makes during this motion, assuming that no slipping occurs. 2. Initially, a ball has an angular velocity of 5.0 rad's counterclockwise. Some time later, after rotating through a total angle of 5.5 radians, the ball has an angular velocity of 1.5 rad/'s clockwise. (a) What is the angular acceleration? What is the average angular velocity? How much time did this take? (b) At some point the angular velocity of the ball had to have been zero. At what angle from it's initial orientation did this occur and how long did it take? 3. In the diagram below, a rope is threaded around three pulleys of radii, R.1 = 0.30 m, R2 = 0.20 m, and R.3 = 0.10 m. There is no slippage. (@) If the rope moves with constant speed v = 5.0 m's, what is the angular velocity of each pulley? What is the frequency and period of each pulley? (b) The rope accelerates from 5.0 m's to 10.0 m/s in 10.0 s, what is the average angular velocity of each pulley for this time? What is the average angular acceleration of each pulley? How many revolutions does each pulley turn in that 10.0 s? R.1