A rope is wound round a hollow cylinder of mass 3 kg and radius 40 cm. What is the angular acceleration of the cylinder if the rope is pulled with a force of 30 N.

Explanation

Torque `tau = Fd sin theta`
`= 30 xx 0.4 xx sin 90^(@)" "(because theta 90^(@))`
`= 30 xx 0.4 xx 1 = 12` Nm
Moment of inertia of the hollow cylinder
`MI = MR^(2) = 3 xx (0.4)^(2) = 0.48 kgm^(2)`
Angular acceleration `alpha = (tau)/(I) = (12)/(0.48) = 25 s^(-2)`