Question

A square plate of mass $120g$ and edge $5.00cm$ rotates about one of the edges. If it has a uniform angular acceleration of $0.2rad/s^2$,

Calculate the torque on the square plate if it rotates about a diagonal with the same angular acceleration.

Answer 1

Given:

The mass of the square plate is $120g$.

The edge of the square is $5.00cm$.

The angular acceleration of the plate is $0.2rad/s^2$.

Moment of inertial of a square plate about its diagonal is

$I=\frac{m{a}^2}{12}$

Here, m is mass of the square plate and a is the edge of the square
Therefore torque produced in the plate is:

$\tau =I\times \alpha$

$I=\frac{m{a}^2}{12}\times \alpha$

$=\left\{\frac{120\times {10}^{-3}\times 5^2\times {10}^{-4}}{12}\right\}\times 0.2$

$=0.5\times {10}^{-5}N-m$.