First slide

Rotational motion

Question

A cord is wound around the circumference of a bicycle wheel (without tyre) of diameter 1 m. A mass of 2 kg is tied to the end of the cord and it is allowed to fall from rest. The weight falls 2m in 4 s. The axle of the wheel is horizontal and the wheel rotates with its plane vertical. $(Take g = 10 {ms}^{- 2})$ then the angular acceleration of the wheel is (rad/s²)

Moderate

Solution

We first find the linear acceleration a by using the relation
$\begin{array}{l} s = ut + \frac{1}{2} {at}^{2} \\ 2 = 0 + \frac{1}{2} \times a \times (4)^{2} \end{array}$
which gives $a = \frac{1}{4} {ms}^{- 2}$ . Now R = 0.5 m. The angular acceleration $α$ is
$α = \frac{a}{R} = \frac{1}{4 \times 0 .5} = \frac{1}{2} = 0 .5 {rads}^{- 2}$
.

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