Question

A uniform rod of mass $m$ and length $L$ lies radially on a disc rotating with angular speed $\omega$ in a horizontal plane about its axis. The rod does not slip on the disc and the center of the rod is at a distance of $R$ from the center of the disc. Find out the kinetic energy of the rod.

Answer 1

Mass of rod$=m$

Length of rod$=L$

Distance between rod's center and axis$=R$

angular velocity$=w$

$\therefore$ Moment of Inertia of rod$=I=\frac{1}{3}m{(R+\frac{L}{2})}^2$

$\therefore K.E=\frac{1}{2}I{w}^2$

$=\frac{1}{2}\left(\frac{1}{3}\right)m{(R+\frac{L}{2})}^2{w}^2$

$=\frac{1}{6}m{(R+\frac{L}{2})}^2{w}^2$