A rope of negligible mass is wound round a hollow cylinder of mass 3 kg and radius 40 cm. What is 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=3kg, R=40 cm=0.40m, F=30N`
Torque: `tau=FxxR=30xx0.40=12Nm`
M.I of the hollow cylinder about its own axis,
`I=MR^(2)=3xx(0.40)^(2)`
`=0.48kgm^(2)`
Angular acceleration,
`alpha=(tau)/1=12/0.48=25 "rad"s^(-2)`
linear acceleration
`a=R alpha=0.40xx25=10ms^(-2)`