A rope of negligible mass 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. ? What is the linear acceleration of the rope ? Assume that there is no slipping.

Explanation

Here M = 3 kg, R = 40 cm = 0.4 m
Moment of inertia of the hollow cylinder about its axis, `I = MR^2 = 3(0.4)^2 = 0.48 kg m^2`
Force applied, F = 30 N.
`therefore " Torque " tau = F xx R = 30 xx 0.4 = 12 N-m`
if `alpha` is angular acceleration produced, then from `tau =Ialpha`
`rArr alpha tau/I = (12)/(0.48) = 25 " rad " s^(-2)`
Linear acceleration , `a = Ralpha = 0.4xx25 = 10ms^(-2