The object rotates about an axis, which we will call the
Torque
is a measure of how much a force acting on an object causes that object
to rotate.pivot
point, and will label 'O'. We will call the force 'F'. The distance
from the pivot point to the point where the force acts is called the moment
arm, and is denoted by 'r'. Note that this distance, 'r',
is also a vector, and points from the axis of rotation to the point where
the force acts. (Refer to Figure 1 for a pictoral representation of these
definitions.) |
Figure 1 Definitions |

Torque is defined as

= **r** x **F** = **r F **sin().

In other words, torque is
the cross product between the distance
vector (the distance from the pivot point to the point where force is applied)
and the force vector, 'a' being the angle between **r** and **F**.

Using the **right hand rule**, we can find the
direction of the torque vector. If we put our fingers in the direction
of **r**, and curl them to the direction of **F**, then the thumb
points in the direction of the torque vector.

Imagine pushing a door to open it. The force of your push (**F**)
causes the door to rotate about its hinges (the pivot point, O). How hard
you need to push depends on the distance you are from the hinges (**r**)
(and several other things, but let's ignore them now). The closer you are
to the hinges (i.e. the smaller **r** is), the harder it is to push.
This is what happens when you try to push open a door on the wrong side.
The torque you created on the door is smaller than it would have been had
you pushed the correct side (away from its hinges).

Note that the force applied, **F**, and the moment
arm, **r**, are independent of the object. Furthermore, a force applied
at the pivot point will cause no torque since the moment arm would be zero
(**r** = 0).

Another way of
expressing the above equation is that torque is the product of the magnitude
of the force and the perpendicular distance from the force to the axis
of rotation (i.e. the pivot point).
Let the force acting on an object be broken up into its tangential (Ftan)
and radial (Frad) components (see Figure 2). (Note
that the tangential component is |
Figure 2 Tangential and radial components of force F |

There may
be more than one force acting on an object, and each of these forces may
act on different point on the object. Then, each force will cause a torque.
**The
net torque is the sum of the individual torques.**

Rotational Equilibrium is analogous to translational equilibrium, where
the sum of the forces are equal to zero. **In rotational equilibrium,
the sum of the torques is equal to zero. In other words, there is no net
torque on the object.**

Here is a useful and interesting interactive activity on rotational equilibrium. Use the "BACK" button to return to this place. Click HERE for the activity.

Example
Illustrating the Right Hand Rule

Example
Problem on Torque

Continue to:Torque
and Angular Acceleration

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