Question

A square plate of mass 120 g and edge 5.0 cm rotates about one of the edges. If it has a uniform angular acceleration of $0.2rad/s^2$, what torque acts on the plate ?

Answer 1

A square plate of mass 120 gm and edge 5 cm rotates about one of the edge.

Let take a small area of the square of width dx and length a which is at a distance from the axis of rotation.

Therefore, mass of that small area

$=\frac{m}{a^2}\times adx$

(m = mass of the square, a = side of the plate)

$l={\int }_0^{a}9{\left(\frac{m}{a}\right)}^2\times a{x}^{2}dx$

$={\left[\left(\frac{m}{a}\right)\left(\frac{x^3}{3}\right)\right]}_0^a$

$={\left[\left(\frac{m}{a}\right)\left(\frac{x^3}{3}\right)\right]}_0^a=\frac{m{a}^2}{3}$

Therefore torque produced

$=l\times a=\left(\frac{m{a}^2}{3}\right)\times a$

$=\left\{\frac{(120\times {10}^{-3}\times 52\times {10}^{-4})}{3.02}\right\}$

$=40\times 25\times {10}^{-7}\times 0.2$

$=0.2\times {10}^{-1}$

$=2\times {10}^{-5}N-m$