First slide

Rolling motion

Question

A thin rod OA of length l is pivoted about a horizontal axis through its lower end O. Initially the rod is held in vertical position. Now the rod is released. What is the angular acceleration of the rod when it makes an angle $30^{o}$ with vertical?

Moderate

A

$\frac{2 g}{3 l}$
B

$\frac{g}{l}$
C

$\frac{3 g}{4 l}$
D

$\frac{4 g}{3 l}$

Solution

M = Moment of mg about O
$= mg . \frac{l}{2} \sin 30^{0} = \frac{1}{4} mg l$
$I_{O} = \frac{1}{3} m l^{2}$
$∴ α = \frac{M}{I_{O}} = \frac{\frac{1}{4} mg l}{\frac{1}{3} m l^{2}} = \frac{3}{4} \frac{g}{l}$

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