To find the direction of a rigid body’s angular acceleration, you must first find the direction of the
body’s angular velocity. Then, if the magnitude of the angular velocity is increasing, the angular
acceleration is in the same direction as the angular velocity vector. On the other hand, if the
magnitude of the angular velocity is decreasing, then the angular acceleration points in the
direction opposite the angular velocity vector.
Rotational Dynamics
Just as we have rotational counterparts for displacement, velocity, and acceleration, so do we have
rotational counterparts for force, mass, and Newton’s Laws. As with angular kinematics, the key
here is to recognize the striking similarity between rotational and linear dynamics, and to learn to
move between the two quickly and easily.
Torque
If a net force is applied to an object’s center of mass, it will not cause the object to rotate.
However, if a net force is applied to a point other than the center of mass, it will affect the object’s
rotation. Physicists call the effect of force on rotational motion torque.
Torque Defined
Consider a lever mounted on a wall so that the lever is free to move around an axis of rotation O.
In order to lift the lever, you apply a force F to point P, which is a distance r away from the axis of
rotation, as illustrated below.
Suppose the lever is very heavy and resists your efforts to lift it. If you want to put all you can into
lifting this lever, what should you do? Simple intuition would suggest, first of all, that you should