0.32 Phy1320: angular momentum -- the mathematics of torque  (Page 7/13)

Similar to Newton's second law

This equation is Newton's second law applied to a system of particles in rotation about a given axis. It makes no assumptions about constant rotationalvelocity.

Torque from an anecdotal viewpoint

One of the objectives of this module is to develop concepts involving rotational motion that are analogous to concepts from earlier modules that involve translationalmotion.

A Lazy Susan

On my dining room table, there is a device that is commonly called a Lazy Susan. In case you are unfamiliar with such devices, it is essentially aturntable. By a turntable, I mean a rather large disk mounted on bearings so that it is free to turn in a plane that is slightly above but parallel with thetop of the dining room table.

The purpose of the Lazy Susan

The purpose of a Lazy Susan is to make it easier to serve food at the dining room table. Various dishes are placed on it . When someone wants a helping ofcarrots, for example, instead of saying "Please pass the carrots," they simply turn the Lazy Susan until they can reach the bowl of carrots and helpthemselves.

Not a module about carrots

However, we won't be discussing how to serve carrots in this module. In this module, I will use the Lazy Susan, in its empty state between meals, to discussvarious aspects of rotating rigid objects.

To make it easier to type the material under discussion, I will refer to the Lazy Susan as a turntable. (For some reason, I can type turntable much morequickly than I can type Lazy Susan.)

Low angular acceleration when coasting

My turntable has pretty good bearings. It is also rather heavy for its size and therefore has a relatively large rotational inertia or moment of inertia, whichever term youprefer.

If you give it a good spin, it will spin for quite a while before all of its rotational energy is dissipated through friction in the bearings and airresistance. By default, therefore, its angular acceleration is low. In other words, the rate of change of its angular velocity is small.

A perpetual motion machine

If we could find a way to eliminate all of the frictional forces acting on the turntable, including air resistance, then it would spin forever. In thatcase, we would have invented what has been called a perpetual motion machine. Therate of change of angular velocity would be zero, meaning that its angular acceleration would also be zero.

Similar to Newton's first law

This reminds us of a moving body that satisfies Newton's first law, which can be paraphrased something like the following:

• a body in motion, being acted upon by no net forces, will continue moving forever in a straight line.

In other words, that law tells us that absent a force to the contrary, a moving body will continue tomove with no change in velocity.

If we could eliminate all of the frictional forces acting on my turntable (which is a rotating body), we might like to say that

• absent any net forces acting on the body, a rotating body with a constant rotational inertia willcontinue rotating with the same angular velocity forever.