Rotational Motion
WHAT IS TORQUE?
Torque is a measure of how much a force acting on an object causes that object to rotate. The object rotates about an axis, which we will call the 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 F sin().

Using the right hand rule, we can find the direction of the torque on an object. 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.

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 give zero torque since there is the moment arm r = 0.
Another way of explaining 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 of force, Ftan is perpendicular to the moment arm, whereas the radial component, Frad, is parallel to the moment arm.) The radial component of the force has no contribution to the torque because it passes through the pivot point (ie. it is parallel to the moment arm). So, only the tangential component of the force affects the torque.

There is an alternate method of calculating torque.


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.

Note that the SI units of torque is a Newton-metre, which is a way of exressing a Joule (units of energy). However, torque is not energy. So, to avoid confusion, we will use the units N.m, and not J. This distinction occurs due to the scalar nature of energy and the vector nature of torque.

Example Illustrating the Right Hand Rule
Example Problem on Torque
Continue to: Torque and Angular Acceleration
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