Moment of Inertia: Derivations & Work Integrals Explained

[stunner5000pt]

First of all i have a final exam tomorrow on Classical Mechanics - Cna someone point out a place that has the derivations of the moments of inertia for various objects

Now if there a disc of mass M spinning about an axis taht is perpendicular to the plane of the disc, and the plane of the disc is horizontal (parallel to Earth's surface) then it's moemnt of inertia is $\frac{1}{2} MR^2$

if there was a little mass located at a point that is r, where r<R from the center of the disc then the moment of inertia is $I = \frac{1}{2} MR^2 + mr^2$
is this correct??

Also , in class my prof said that on the exam he would have a question in which we would have to calculate a work integral... what is that ??
as far as I am concerned $W = \int F \cdot d$ is there anything more to it?? Can you point out an example of something that is more complicated liek that??

 

[dextercioby]

So the little mass is standing on the disk?It's okay,then...

Daniel.

 

[thepatientmental]

Yes, your calculation for the moment of inertia of a disc is correct. As for finding derivations of moments of inertia for various objects, a good place to start would be your textbook or class notes. You can also search online for specific objects and their moments of inertia, as there are many resources available.

A work integral is a way to calculate the work done by a variable force over a certain distance. It involves integrating the force function with respect to the distance traveled. An example of a more complicated work integral could be calculating the work done by a spring with varying stiffness over a certain displacement. In this case, the force function would be a function of displacement and you would have to integrate it over the given displacement range. I suggest practicing some examples from your textbook or class notes to get a better understanding of work integrals.