Consider a rigid body capable of rotating about the z-axis through O. Let a force act on the body in the xy -plane at some point P whose position vector with respect to O is . If d is the perpendicular distance of the line of action of the force from the axis, then the torque acting on the body due to this force is defined as
= Fd = Fr sin q
Torque is also called the moment of force and it is a measure of the turning effect of force about the given axis. The same force produces a larger turning effect, if its line of action is farther from the axis. Torque is actually a vector quantity having magnitude rF sinq and having direction along the axis of rotation. In vector notation, it is written as
Torque is rotational analogue of force. A rigid body is a system of particles in which the distances between the particles are fixed.
Basic equation of Rotation
The relation t = Ia is the fundamental equation of rotation. It is the exact counterpart of the equation F = ma in linear motion. An unbalanced torque is necessary to give a body an angular acceleration just as an unbalanced force is required to give a body a linear acceleration. The quantities t, I and a play similar roles in angular motion as F, m and a play in translatory motion. Therefore for rotational motion we use
t = Ia
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