Torque and Angular Acceleration
1. A child is pushing a merry-go-round. The angle through the merry-go-round has turned varies with time according to θ(t) = γt + βt3, where γ = 0.400 rad/s and β = 0.0120 rad/s3.
a. Calculate the angular acceleration as a function of time.
b. What is the initial value of the angular velocity?
c. Calculate the instantaneous value of the angular velocity at t =5.00 s and the average angular velocity for the time interval t = 0 to t = 5.00 s.
2. At t = 0 the current to a dc electric motor is reversed, resulting in an angular displacement of the motor shaft given by to θ(t) = (250 rad/s)t - (20.0 rad/s2)t2 – (1.50 rad/s3)t3.
a. At what time is the angular velocity of the motor shaft zero?
b. Calculate the angular acceleration at the instant that the motor shaft has zero angular velocity.
c. How many revolutions does the motor shaft turn through between the time when the current is reversed and the instant when the angular velocity is zero?
d. How fast was the motor shaft rotating at t =0, when the current was reversed?
e. Calculate the average angular velocity for the time period from t = 0 to the time calculated in part a.
3. A wheel is rotating about an axis that is in the z direction. The angular velocity is – 6.00 rad/s at t = 0, increases linearly with time, and is +8.00 m/s at t = 7.00 s. We have taken counterclockwise rotation to be positive.
a. Is the angular acceleration during this time interval positive or negative?
b. During what time interval is the speed of the wheel increasing? Decreasing?
c. What is the angular displacement of the wheel at t = 7.00s?
4. A turntable rotates with a constant 2.25 rad/s2 angular acceleration. After 4.00 s it has rotated through an angle of 60.0 rad. What was the angular velocity of the wheel at the