Define Torque and derive its expression.

Explanation

(i) Torque is defined as the moment of the external applied force about a point or axis of rotation.
(ii) `vec(tau) = vec(r) xx vec(F)` where `vec(r)` is the position vector of the point and the force `vec(F)` is acting on the body as shown in Figure.

(iii) Here, the product of `vec(r) and vec(F)` is called the vector product or cross product. The vector product of two vectors results in another vector that is perpendicular to both the vectors. Hence, torque `(vec(tau))` is a vector quantity.
(iv) Torque has a magnitude (r F `sin theta`) and direction perpendicular to `vec(r) and vec(F)`. Its unit in N m.
`vec(tau) = (r F sin theta) hat(n)`
(v) Here, `theta` is the angle between `vec(r) and vec(F) and hat(n)` is the unit vector in the direction of `(vec(tau))`.