Define Torque and derive its expression.

1.	Define Torque and derive its expression.
Answer» Solution :(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))`.

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