A rope of negligible mass is wound round a hollow cylinder of mass 3kg and radius 40 cm. What is the angular acceleration of the cylinder if the rope is pulled with a force of 30N? What is the linear acceleration of the rope? Assume that there is no slipping.

Explanation

Here M = kg, R = 40 cm = 0.4 m
Moment of inertia of the hollow cylinder about its axis
`I=MR^(2)=3(0.4)^(2)=0.48kgm^(2)`
Force applied F = 30 N
`therefore` Torque, `tau=FxxR=30xx0.4=12N-m`.
If `alpha` is the angular acceleration, produced, then from `tau=lalpha`
`alpha=(tau)/(l)=(12)/(0.48)=25" rads"^(-2)`
Linear acceleration, `a=Ralpha=0.4xx25`
`=10m//s^(2)`.