Torque

In translational motion, a force, , is required to produce a change in translational motion, i.e. an acceleration:

= m

where m is the mass and is the linear acceleration. (Newton's Second Law).

In complete analogy, in rotational motion a torque, , is required to produce a change in rotational motion,

= I

where I is the moment of inertia (we will explain later in much more detail what this is), and is the angular acceleration. Please note that the torque is a vector quantity, as is the angular acceleration. They point in the same direction.

A torque is the cross product between force and moment arm - it is produced by exerting a force F with a moment arm r>:

= x = r F t = r F sin$\theta$ $\tau$

Here r = r sin$\theta$ is the moment arm or the perpendicular line of action of the force F. Another way of saying this: r sin$\omega$ is the component of that is perpendicular to the force vector . The torque points in a direction $\tau$ that is both perpendicular to the vector and to the vector .

You can again use the right-hand-rule (see figure on the right) of the cross product to determine which way the torque is pointing. So if and are in the plane as shown, and the middle finger points out of the screen, that means that the torque is counterclockwise. A middle finger pointing into the screen would correspond to a clockwise torque.

The magnitude of the torque from the above equation is:

$\tau$= r F sin$\theta$

© MultiMedia Physics, 1999