A rope of negligible mass is wound around 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 = 3kg, R = 40cm = 0.4m`
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 = 30N :.` Torque, `tau = F xx R = 30 xx 0.4 = 12 N-m`
If `alpha` is angualr acceleration produced, then from `tau = I alpha`
`alpha = (tau)/(I) = (12)/(0.48) = 25 rad s^(-2)`
linear acceleration, `a = R alpha = 0.4 xx 25 = 10 ms^(-2)`