Inertia

[Red_CCF]

Hi

If the moment of inertia exist to resist a body to change from its rotational motion and linear inertia exists to resist a body's change from its linear motion, then for a point mass on a rotating body, which inertia does it obey?

Thanks.

[Doc Al]

Both, of course. Mass exhibits both linear and rotational aspects of inertia at the same time.

[Red_CCF]

Both, of course. Mass exhibits both linear and rotational aspects of inertia at the same time.

But how can it satisfy linear inertia if it wants to satisfy rotational inertia and vice versa; like how can it want to go both straight and in a circle at the same time?

[Doc Al]

But how can it satisfy linear inertia if it wants to satisfy rotational inertia and vice versa; like how can it want to go both straight and in a circle at the same time?
I don't understand what you mean. The same object has both linear and rotational inertia at the same time. It's not either or.

Perhaps you can give a specific example?

[Studiot]

I don't know if DocAl meant that a point mass has rotational inertia about its own axis and can thus spin and translate at the same time.

But the thing to remember is that there are two 'components' to inertia. Viz the resistance to change of the body itself and the nature of the forcing or changing agent.

We can calculate a moment of inertia about any axis we choose, but it does not mean there is an agent acting to cause rotation about this axis. Similarly we can calculate a linear inertia (mass) in any direction we choose ( they are usually the same in all directions) but there is only an effect if there is a force acting in that direction.

[Danger]

I can't help wondering whether or not Red is confused regarding rotation vs. revolution.

[Doc Al]

I don't know if DocAl meant that a point mass has rotational inertia about its own axis and can thus spin and translate at the same time.
That's not what I meant. The rotational inertia of a point mass about its own axis would be zero. But a point mass can certainly have rotational inertia about some other axis.

[Red_CCF]

That's not what I meant. The rotational inertia of a point mass about its own axis would be zero. But a point mass can certainly have rotational inertia about some other axis.

I think I figured out what I was confused about. I was thinking that for a particle rotating about an axis, to satisfy its inertia in rotational motion would mean that it couldn't satisfy its inertia in linear motion since its velocity would be changing directions.

I think it arises from my (poor) understanding of fictitious centrifugal force as the linear inertia resists the change in velocity but yet a particle has an rotational inertia.

[Studiot]

One interpretation of inertia is a measure of the energy required to stop a body doing whatever it is doing.

A particle that is spinning, but not translating, has more energy, by virtue of its spin, than a similar one that is also not spinning.

It would take energy to stop the spin. Do you not count this as a manifestation of inertia?

[Doc Al]

I think I figured out what I was confused about. I was thinking that for a particle rotating about an axis, to satisfy its inertia in rotational motion would mean that it couldn't satisfy its inertia in linear motion since its velocity would be changing directions.

I think it arises from my (poor) understanding of fictitious centrifugal force as the linear inertia resists the change in velocity but yet a particle has an rotational inertia.
The particle rotating about an axis is behaving just as you'd expect: It's linear momentum is changing since the object it's attached to is exerting a centripetal force on it.

[Danger]

Another thing to keep in mind, now that the parameters have been defined, is that "spin" is a physicist's expression for a particle property that does not involve "spinning" as in the sense of a top or curveball. By the same token, you can't say that a particular quark is "charming", although "charm" is one of its characteristics.

[Studiot]

'spin' is also used by children playing with tops, cricket and tennis players - USW

[Danger]

Well, it gets into weird stuff like I3, which I believe is properly referred to as "the vertical component of isotopic spin". WTF?!