The math help thread

All righty. So, I really don't understand this rotation stuff that much, so it'd be much appreciated if someone were to guide me through this.

A uniform sphere of radius R and mass M rotates freely about a horizontal axis that is tangent to an equatorial plane of the sphere, as shown below. What is the moment of inertia of the sphere about this axis?



I'm assuming a 'uniform sphere' means it's solid? And also, would this qualify for the institution of the Parallel Axis Theorem? I'm not even sure.

If it is, I'd say that:

I = 2/5 M*R^2 + M*R^2 = 7/5 M*R^2 ?

Two more.

Use the Parallel-Axis Theorem to calculate the rotational inertia at the position shown in the figure below... m=20kg


From what I learned, you need to do something about making it a thin rod rotating at one end, but I'm stuck after that. Is it just the moment of inertia of the rod rotating from one end or is there something else to it?

Annd..

Using the figure below, derive an expression for the velocity of center of mass of the solid cylinder (disk) as it rolls down the incline. Also show the derivation for the linear acceleration of the center of mass.



Yeah, lost.