Question

A light rod of length 1 m is pivoted at its centre and two masses of 5 kg and 2 kg are hung from the ends as shown in figure (10-E3). Find the initial angular acceleration of the rod assuming that it was horizontal in the beginning.

Answer 1

$\tau =I_{net}\times \alpha$

$\Rightarrow F_1{r}_1-F_2{r}_2=(m_1{r}_1^2+m_2{r}_2^2)\times \alpha$

$\Rightarrow -2\times 10\times 0.5+5\times 10\times 0.5$

$=[5{\left(\frac{1}{2}\right)}^2+2{\left(\frac{1}{2}\right)}^2]\alpha \Rightarrow 15=\frac{7}{4}\alpha$

$\Rightarrow \alpha =\frac{60}{7}=8.57{\text{rad/s}}^2$