What is torque? Derive an expression for the torque acting on a rotating body.

Hint: Let us first get some basic idea regarding torque In physics and mechanics, torque is the rotational analogue of linear force. It's also known as the moment, moment of force, rotational force, or turning effect, depending on the subject of research.

Complete step by step answer:
Archimedes' study of the use of levers gave birth to the concept. A torque is a twist of an item around a given axis, similar to how a linear force is a push or a pull. The product of the magnitude of the force and the perpendicular distance of the line of action of a force from the axis of rotation is another definition of torque. Torque is usually denoted by the letter $\tau $, which is the lowercase Greek letter tau. When the term "moment of force" is used, it is usually abbreviated as $M$.

Moment of force, often known as torque, is the turning effect of a force. It is calculated using the product of the force and the perpendicular distance between the line of force action and the axis of rotation.
Thus torque $ = $ force $ \times $ perpendicular distance from the axis of rotation.
Torque $\tau = F \times r$ $mar = m{r^2}a$
$\because a = r\,\,a$
Torque for entire body $\tau = \left( {\sum {m{r^2}} } \right)a = Ia$
$\therefore m{r^2} = I$, the moment of inertia and $a$ is angular acceleration.

Note: The torque is a pseudovector in three dimensions, and it is given by the cross product of the position vector (distance vector) and the force vector for point particles. The force applied, the lever arm vector connecting the point around which the torque is being measured to the point of force application, and the angle between the force and lever arm vectors determine the magnitude of torque in a rigid body.