haruspex's latest activity

I get the same. Curiously, that gives 0 for ##5R=7r##.

But I am arguing that you cannot arrive at it using your approach rather than mine because the steps you have to take to find the...

I am saying that you cannot apply it to find the moment of inertia of the ball's motion about C. You can apply it, as @kuruman notes...

An implication of my previous post is that you should think of moment of inertia as resistance to angular acceleration about the axis...

As I wrote in post #28, the moment of inertia of a body is only of interest in the context of rotation about some axis. To put that...

We have to assume the sphere has uniform density, so the mass distribution does not change.

Yes, but when you say "about axis C" what you mean is that to accelerate it angularly about C at rate ##\alpha## as a rigid body (that...

Your approach was to take moments about C, but as I have shown that is awkward because you cannot apply the parallel axis theorem...

The parallel axis theorem applies to a rigid body rotating, as a whole, about a given axis. In this problem, the sphere is not doing...

Yes, because in that view all parts of the sphere are rotating about the same axis as a unit. But I think you do have to be careful...

Of course, but it is only of interest in the context of rotation about some axis. It doesn’t have 'a' moment of inertia in that sense...

Your mistake is in applying the parallel axis theorem. That is only valid for a rigid body rotating as a unit about the axis. It would...

Yes, if you take the same sense as positive for both, but no law says you have to. If ##\theta## is the angle clockwise from vertical...

My wording was sloppy; I should have said "for accelerating up the slope". AI's rolling equation is ##\alpha r=(R-r)\ddot\theta##. If it...

No, ##\Delta s## is greater than that because of the curved surface. Consider e.g. R only marginally greater than r.