Torque and Rotational Equilibrium

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.

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