First slide

Rotational motion

Question

One end of a straight uniform 1 m long bar is pivoted on horizontal table. It is released from rest when it makes an angle $30^{0}$ from the horizontal (see figure) . Its angular speed when it hits the table is given as $\sqrt{n} s^{- 1}$ , where n is an integer. The value of n is

Moderate

Solution

According to conservation of energy
$\begin{array}{l} m g (\frac{l}{2}) \sin θ = \frac{1}{2} I_{p} ω^{2} h e r e I_{P} = \frac{m l^{2}}{3} \\ \Rightarrow ω = \sqrt{\frac{3 g}{2 l}} = \sqrt{\frac{3 \times 10}{2 \times 1}} = \sqrt{15} r a d / s \end{array}$

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