What is rotational motion?

Rotational motion is motion which follows a curved path.

This is in stark contrast with linear motion, which follows straight paths. Linear motion is generally one's first introduction into the physics of motion. There are many parallels to be made between the two.

Linear motion is primarily concerned with displacement, velocity, , momentum, and force. In comparison, rotational motion primarily deals with angular displacement, angular velocity and acceleration, , and . Each of these can be seen as definite parallels to the case of linear motion. For example:

##v = (Deltax)/(Delta t) ## is the classical definition of velocity.

## omega = (Delta theta)/(Delta t)## is the definition of angular velocity, as the rate of change of angle. Notice how similar the definitions appear.

## F = (Delta p)/(Delta t) = m a ## is the definition of force in linear dynamics.

## tau = (Delta L)/(Delta t) = I alpha## is the rotational analogue. We have angular momentum ##L## as a counterpart to linear momentum ##p##, ##I## as analogue to mass, and angular acceleration ##alpha## to compare to normal acceleration.

The prime example of rotational motion is , whereby the path rotates about a fixed axis. However, rotational motion can also be more complicated and follow any curve as a path. This is known by the general name curvilinear motion.

It is often a misconception of students that we can either have rotational motion or linear motion. The truth is that they are both just different ways of demonstrating the same thing.

One of the fundamental results from calculus is that any continuous curve can be locally approximated by a straight line. This is where the description with linear motion comes in. As it turns out we can also approximate curves locally with parts of a circle! This is where rotational motion comes in. For most purposes, we use a combination of both descriptions to get a detailed understanding of the motion, however, sometimes one description might be more convenient than the other.