It is a physical quantity similar to force in Linear motion which represents the its effect on the rotatory motion of a body. If the body is fixed at a point or along a line, it has only rotational motion. Force is needed to change the translational state of a body, i.e. to produce linear acceleration.
In the case of rotatory motion it is not only the force that determines the motion and also its position at which it is applied.
Example :
Let opening or closing of a door is the case . A door is a rigid body which can rotate about a fixed vertical axis passing through the hinges. Unless a force is applied the door does not rotate. But any force does not do the job. A force applied to the hinge line cannot produce any rotation at all, whereas a force of given magnitude applied at right angles to the door at its outer edge is most effective in producing rotation. It is not the force alone, but how and where the force is applied is important in rotational motion.
Torque is also called as moment of force. The meaning of moment is always multiply with displacement. That means torque is the vector product of force and displacement.
Expression :
If a force acts on a single particle at a point P whose position with respect to the origin O is given by the position vector r , the moment of the force acting on the particle with respect to the origin O is defined as the vector product
τ = r × F
The moment of force (or torque) is a vector quantity. The symbol τ stands for the Greek letter tau. The magnitude of τ is τ = rF sinθ
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.
If τ = 0 if r = 0, F = 0 or θ = 00 or 1800 . 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.
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.
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