Question

A flywheel in the form of a uniformly thick disk of radius 1.63 m, has a mass of 27.6 kg and spins counterclockwise at 489 rpm. Calculate the constant torque required to stop it in 4.25 min.

Answer 1

Mass of the flywheel = M = 27.6 kg

Radius of the flywheel = R = 1.63 m

Moment of inertia of the flywheel = I

I = 36.665 kg.m²

Initial angular speed of the flywheel = ₁ = 489 rpm = 489 x (2/60) rad/s = 51.208 rad/s

Final angular speed of the flywheel = ₂ = 0 rad/s (Comes to a stop)

Time period in which the flywheel is brought to a stop = t = 4.25 min = 4.25 x (60) sec = 255 sec

Angular acceleration of the flywheel =

= -0.2008 rad/s²

Negative as it is deceleration.

Constant torque applied to the flywheel =

= -7.36 N.m

The negative sign indicates that the torque is acting against the motion of the flywheel.

Constant torque required to stop the flywheel in 4.25 min = -7.36 N.m