the origin O is defined as the vector product τττττ = r × F ( . ) The moment of force (or torque) is a vector quantity. The symbol τ τ τ τ τ stands for the Greek letter tau . The magnitude of τ τ τ τ τ is τ = r F sin θ ( .24a) where r is the magnitude of the position vector r , i.e.
the length OP, F is the magnitude of force F and θ is the angle between r and F as shown. Moment of force has dimensions M L T - . Its dimensions are the same as those of work or energy. It is, however, a very different physical quantity than work.
Moment of a force is a vector, while work is a scalar. The SI unit of moment of force is newton metre (N m). The magnitude of the moment of force may be written ( sin ) r F ⊥ ( .24b) or sin r F rF ⊥ ( .24c) where r ⊥ = r sin θ is the perpendicular distance of the line of action of F from the origin and sin ) ⊥ = is the component of F in the direction perpendicular to r . Note that τ = if r = , F = or θ = or .
Thus, the moment of a force vanishes if either the magnitude of the force is zero, or if the line of action of the force passes through the origin. One may note that since r × F is a vector product, properties of a vector product of two vectors apply to it. If the direction of F is reversed, the direction of the moment of force is reversed. If directions of both r and F are reversed, the direction of the moment of force remains the same.
. . Angular momentum of a particle Just as the moment of a force is the rotational analogue of force in linear motion, the quantity angular momentum is the rotational analogue of linear momentum. We shall first