A flywheel in the form of a uniformly thick disk of radius 1.48 m, has a mass of 28.6 kg and spins counterclockwise at 277 rpm. Calculate the constant torque required to stop it in 2.50 min.
First thing’s first: convert your revolutions per minute angular velocity to radians per second. Equivalent angular velocity (w) is 182.2 rad/s. Very important to our next equations.
We need to figure out how much angular deceleration we need to stop this wheel exactly in 2.5 minutes. Now, recall your kinematics formulae: w = w initial + at. Here, t is 2.5 min (converted to 150 sec), w is 0, and w initial is 182 rad/s. Now from here, it’s easy to figure out.
0=182.2 + 150a
a = -1.214
We can assume the moment of intertia (I) here is 0.5MR^2, which gives us 31.32 for I. Since torque=Ia, we need a torque of roughly 38.0 N*m. And that’s our answer, 38.0 Nm.