 Copyright © Michael Richmond. This work is licensed under a Creative Commons License.

## Torque and Rotational Equilibrium

• There are rotational analogs to Newton's Laws of Motion:

1. An object at rest, remains at rest (not rotating); an object rotating, continues to rotate with constant angular velocity; unless acted on by an external torque.

2. ```           torque = (moment of inertia) * (angular acceleration)
```
• In these equations, torque takes the place of force. Just as force is that which makes objects accelerate linearly, torque is that which makes objects accelerate rotationally.
• One can calculate the torque exerted by a force around an axis of rotation via
```              torque   =  (force) * (lever arm)
```
where
```              torque         is the torque, in Newton-meters

force          is the force applied, in Newtons

lever arm      is the "effective distance" from the point
of force to the axis of rotation
```
• If the force is applied perpendicular to the radius vector running from axis to point of force, then the lever arm is simply the radius r; but if the force is applied at an angle theta to the radius vector, then the lever arm is r * sin(theta).
• An object in rotational equilibrium has no net external torque:
```             sum of all external torques  =  0
```
Remember that "rotational equilibrium" may mean that the object is not rotating ... or it may mean that the object is rotating with constant angular velocity.
Viewgraphs             Copyright © Michael Richmond. This work is licensed under a Creative Commons License.