Question

A light rigid rod of length $4m$ is connected rigidly with two identical particles each of mass $m=2kg$, the free end of the rod is smoothly pivoted at O. The rod is released from rest from its horizontal position at $t=0$. Find the angular acceleration of the rod at $t=0$.$\left(inrad{s}^{-2}\right)$

Answer 1

Let angular acceleration be $\alpha$.

${\tau }_o=I_o\alpha$

$mg\left(2\right)+mg\left(4\right)=\left[m\right(2{)}^2+m\left(4{)}^2\right]\alpha$

$6mg=\alpha \times 20m$

$⟹\alpha =3rad/s^2$