# A flywheel in the form of a uniformly thick disk

Asked by wiki @ in Physics viewed by 127 People

A flywheel in the form of a uniformly thick disk of radius 1.83 m, has a mass of 24.1 kg and spins counterclockwise at 217 rpm. calculate the constant torque required to stop it in 2.25 min.

We need to calculate the angular acceleration of the disk first.
The disk starts at 217 rpm and stops, so its final angular speed is zero, therefore the variation of angular speed is

The time interval in which the disk stops is

Therefore, the angular acceleration is

Now, we can find the torque needed to stop the disk by using the equivalent of Netwon's second law for the rotational motions:

where is the torque, is the moment of inertia of the object and is the angular acceleration.
The moment of inertia for a disk is , therefore substituting this into the formula and by using the data of the exercise, we can find the torque:

where the negative sign means the torque is directed against the direction of the rotation, so anti-clockwise.

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