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 0.20 rad/s². what torque acts on the plate.?

Answer 1

Given in the question :-

Angular acceleration , α = 0.20

Mass M = 120 g or 0.12 kg

Edge a = 5.0 cm or 0.05 m

Moment of inertia of plate when line passing by centre and parallel to the edge

I =Ma²/12

Moment of Inertia (Plate edge)

$I' = I+M(a/2)^2$

$= \frac{Ma^2}{12}+\frac{ Ma^2}{4}$

=Ma²/3

Now putting the values,

=(0.12 × 0.05 × 0.05)/3

= 0.0001 kg.m²

Torque (plate) = I'α

=0.0001 × 0.20

=2 x 10⁻⁵ N.m

Hope it Helps :-)