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  4. A uniform metre stick of mass M is hinged at one end and supported in a horizontal direction by a string attached to the other end. What should be the initial acceleration (in rad / s 2) of the stick if the string is cut?

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Q. A uniform metre stick of mass $M$ is hinged at one end and supported in a horizontal direction by a string attached to the other end. What should be the initial acceleration (in $rad / s ^{2}) $ of the stick if the string is cut?

System of Particles and Rotational Motion

Solution:

$\tau=I \alpha=M g \frac{L}{2}$
$\frac{M L^{2}}{3} \alpha=\frac{M g L}{2}$
$\Rightarrow \alpha=\frac{3 g}{2 L} rad / sec ^{2}$