Work–kinetic energy theorem for rotational motion. need to be symetri?

[07685gg]

Why it need to be symetric
From the book Physics - Serway
Thanks

Edit:
I'm bringing just the statement from Serway's Physics 9th p 313

 

[D H]

That image was a bit too much. It's oversized for one thing, and for another that's verging on copyright violation.

Try again, with words rather than an image. Give a reference to the book (name, author, page number) and summarize the parts you don't understand. You can quote a paragraph or two, but an entire photocopied page is just too much.

I reopened the thread. Please try to summarize your concerns in words, not with a scanned image, and we'll do our best to try to answer your questions.

 

[D H]

The next time you post a scanned image, please try to resize your images so they're a bit smaller than this -- 640 by 480 or so.


The reason it has to be symmetric in that freshman level physics text is that freshman do not yet have the mathematical skills to cover the full problem. The problem is that ultimately moment of inertia is not a scalar. It is instead a second order tensor. You haven't studied tensors. You might *start* studying them in a couple of years. There is nothing in that more advanced treatment that necessitates that an object be symmetric.

By making the object in question symmetric, moment of inertia can essentially be treated as if it was a scalar, just like mass. This simplifies the problem of rotational motion to something that is understandable at a freshman physics level.

 

[07685gg]

cool. making sense

(I would expect from the author to be more clear about that)

 

[PJC01]

:

The work–kinetic energy theorem for rotational motion states that the work done by the net torque acting on a rigid body is equal to the change in the body's rotational kinetic energy. This theorem applies to both symmetrical and non-symmetrical objects, as long as they are rigid bodies.

The reason why it needs to be symmetrical is because the rotational kinetic energy of a rigid body depends on its moment of inertia, which is a measure of how its mass is distributed around its axis of rotation. If the body is symmetrical, its moment of inertia will be the same for all rotations around its axis, making the calculation of its rotational kinetic energy simpler and more consistent.

On the other hand, if the body is non-symmetrical, its moment of inertia will vary for different rotations, making the calculation more complex and potentially leading to errors. Therefore, in order to accurately apply the work–kinetic energy theorem for rotational motion, it is important for the body to be symmetrical.