        THE LAWS OF ROTATIONAL MOTION

 motion: TOC for Knowledge Concepts, Exercises, and Solutions

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Everything spins.  Mathematically, rotational motion follows a set of laws that
parallels Newton's Laws for linear motion.

L = r x p    (angular momentum = cross product of radius and linear momentum)
= mvr      ( = linear momentum * radius for a circular orbit)

T = r x F    (torque = cross product of radius and force)
= mar      ( = linear force * radius for a circular orbit)

a = v^2/r    (centripetal acceleration = orbital velocity squared / radius)

F = mv^2/r   (centripetal force = mass of object * centripetal acceleration)

Analogous to the principle of conservation of momentum is the principle of
conservation of angular momentum: an object will move with constant orbital
or rotational velocity unless acted upon by an outside torque.  When an
object is being held in motion around another object by a central force --
for example, the pull of a rope, or gravity -- its velocity is related to
its acceleration.  A third law of rotational motion states that for every
(centripetal) force pulling inward toward the center of rotation, there is and
equal and opposite (centrifugal) force pushing outward toward from the center of
rotation.

To summarize:

The first law is the Conservation of Angular Momentum.
Thus, if T = 0, then L = mvr.
The second law is the definition of torque.
Thus, if T does not = 0, then T = mar.
The third law is the Reaction Principle. Again, there is no simple formula, but it
is a fundamental and important rule of rotational motion.

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