A flywheel in the form of a uniformly thick disk of radius 1.23 m has a mass of 93.6 kg and spins counterclockwise at 369 rpm. Calculate the constant torque required to stop it in 2.25 min.

20.26 Nm

Explanation:

r = 1.23 m, m = 93.6 kg, w = 0, f0 = 369 rpm = 369 / 60 = 6.15 rps

w0 = 2 x 3.14 x 6.15 = 38.622 rad/s

t = 2.25 min = 2.25 x 60 = 135 second

Moment of inertia = 1/2 m r^2 = 0.5 x 93.6 x 1.23 x 1.23 = 70.8 kg m^2

use first equation of motion for rotational motion

w = w0 + α t

0 = 38.622 - α x 135

α = 0.286 rad/s^2

torque = moment of inertia x angular acceleration

Torque = 70.8 x 0.286 = 20.26 Nm