#### Question

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.

#### Solution

Mass of the hollow cylinder, *m* = 3 kg

Radius of the hollow cylinder, *r* = 40 cm = 0.4 m

Applied force, *F* = 30 N

The moment of inertia of the hollow cylinder about its geometric axis:

*I* = *mr*^{2}

= 3 × (0.4)^{2} = 0.48 kg m^{2}

Torque, t = F x r

= 30 × 0.4 = 12 Nm

For angular acceleration `alpha`, torque is also given by the relation:

`t = Ialpha`

`alpha = t/I = 12/0.48`

`= 25 " rad s"^(-2)`

Linear acceleration = `ralpha = 0.4 xx 25 = 10 ms^(-2)`

Is there an error in this question or solution?

Solution 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. Concept: Moment of Inertia.