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Physics 1120 In-Class Problems: Rotational Kinematics

  1. 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?

  2. In the diagram below, a rope is threaded around three pulleys of radii, R1 = 0.30 m, R2 = 0.20 m, and R3 = 0.10 m. There is no slippage.
    (a) 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?

  3. Two rotating disks, each with a visible dot, are show at the same instant in time in the figure below. The disk on the left has zero initial angular velocity and an angular acceleration of α = 12.0 rad/s2. The disk on the right has a constant angular velocity of ω = 18.0 rad/s. When will the two disks have turned through the same total angle? How many revolutions will this have taken for each disk? If the disks had different radii, would there be any change to your answers?

  4. A ball is thrown into the air at an angle of 25° to the horizontal with a velocity of 11.0 m/s. As the ball leave the pitcher's hand it has an angular velocity of 35.0 rad/s. How many revolutions does the ball make before it returns to the same level? Note that the x, y, and rotational motions are all completely independent. Also note that the linear velocity given is not the velocity in the equation v = ωR.

  5. A motorcycle has tires with a diameter of 44.0 cm. Cruising down the highway, they are rotating at 1150 rpm (revolutions per minute). What is the angular velocity in radians per second? What is the frequency and period of the tires? What is the tangential velocity of the edges of the tires (and hence the linear velocity of the motorcycle) in m/s and km/h?

  6. A bicyclist uniformly increases his pedaling from 30 rev/min to 120 rev/min in 5.0 s. For that time interval determine:
    (a) the linear acceleration of the bike,
    (b) the final linear speed of the bike, and
    (c) the distance traveled by the bike.

    As shown in the diagram below, the pedal gear has a radius of 12.0 cm, the back wheel gear has a radius of 3.5 cm, and the back wheel itself has a radius of 38.0 cm.


  7. The wheels in the diagram below have radii R1 = 45 cm, R2 = 12 cm, R3 = 32 cm, and R4 = 9 cm. Wheel 1 accelerates from rest at α = 6 rad/s2. A fter t = 12 seconds, find the angular displacement of wheel 4.

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