A spinning cylinder has a moment of inertia of 22.2 kg m^2. How much torque is requred to slow down from an angular velocity of 111 rad/sec to 33.0 rad/sec in only 4.40 seconds?
To calculate the torque required to slow down the spinning cylinder, we can use the formula:
Torque = (Change in angular momentum) / (Change in time)
First, we need to calculate the change in angular momentum:
Initial angular momentum = I * ω1 = 22.2 kg m^2 * 111 rad/sec = 2464.2 kg m^2/sec
Final angular momentum = I * ω2 = 22.2 kg m^2 * 33.0 rad/sec = 732.6 kg m^2/sec
Change in angular momentum = Final angular momentum - Initial angular momentum
Change in angular momentum = 732.6 - 2464.2 = -1731.6 kg m^2/sec
Next, we can calculate the torque:
Torque = Change in angular momentum / Change in time
Torque = -1731.6 kg m^2/sec / 4.40 sec
Torque = -393.9 Nm
Therefore, the torque required to slow down the spinning cylinder from an angular velocity of 111 rad/sec to 33.0 rad/sec in 4.40 seconds is 393.9 Nm.