Q7.14     A rope of negligible mass is wound round a hollow cylinder of mass 3kg  and radius
              40cm . 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.

Answers (1)

The moment of inertia is given by :

                                                           I\ =\ mr^2

or                                                              =\ 3\times (0.4)^2\ =\ 0.48\ Kg\ m^2

And the torque is given by : 

                                                          \tau \ =\ r\times F

                                                                =\ 0.4\times 30\ =\ 12\ Nm

Also,                                                \tau\ =\ I\alpha

So                                                   \alpha \ =\ \frac{\tau }{I}\ =\ \frac{12}{0.48}\ =\ 25\ rad/s^{-2}

And the linear acceleration is         a\ =\ \alpha r\ =\ 0.4\times 25\ =\ 10\ m/s^{-2}

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