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

`M=3kg, R=40xx10^(-2)m`
(i) MI of hollow cylinder about its own axis
`I=MR^(2)`
`=3xx(40xx10^(-2))^(2)`
`=48xx10^(-2)kgm^(2)`
Torque `tau=FxxR`
So, `tau=30xx40xx10^(-2)`
`tau=Ialpha`
So, `tau=12`
`alpha=(12)/(I)=(12)/(48xx10^(-2))=(100)/(4)=25 "rad" s^(-1)`
`(ii) F=ma`
`a=(F)/(m)=(30)/(3)=10 ms^(-2)`