Angular Momentum and Point of Application in Rolling Motion

[PhizKid]

Homework Statement

Homework Equations

Angular momentum

The Attempt at a Solution

So I have my work shown in the two pictures. r_m, r_f denote the position vectors to the center of mass and point of application of force respectively (with respect to the chosen origin of course). Is this the way to do it? I've seen a way done by some others where they take the origin of the coordinate system to be instantaneously co - moving with the point on the ball that is in contact with the ground (so that again torque will vanish with respect to this origin because it acts at the origin itself) and use the exact same terms for the final and initial angular momentum. This frame will however be accelerating with respect to a fixed coordinate system due to friction but is angular momentum unaffected by this?

 

[haruspex]

It's a bit hard to comment on the other approach without seeing it in detail.

 

[PhizKid]

Is my method correct however? Also there wasn't any difference at all in the other approach other than the fact that the reference point is taken to be the point of contact of the ball with the ground. The equations are then written the same way. I was just wondering if that was allowed because such a reference point would be decelerating with respect to a fixed one.

 

[haruspex]

Is my method correct however?

I believe it is, and a quite interesting one too.

Also there wasn't any difference at all in the other approach other than the fact that the reference point is taken to be the point of contact of the ball with the ground. The equations are then written the same way. I was just wondering if that was allowed because such a reference point would be decelerating with respect to a fixed one.

It's still unclear without seeing the details. I often take moments about a point of contact, but treating it only as the instantaneous point of contact. That's not the same as using an accelerating point as the origin of a reference frame. Even in the latter case, it might happen to be valid, but probably should be supported by some argument as to why it is valid.

 

[PhizKid]

Could you explain how you would do it with the way you mentioned by keeping the origin instantaneously at rest with respect to the point of contact. Thanks haruspex!

 

[haruspex]

Could you explain how you would do it with the way you mentioned by keeping the origin instantaneously at rest with respect to the point of contact. Thanks haruspex!

No, I didn't necessarily mean for this problem. I meant rotational dynamics problems in general. For a rolling ball or disc, the point of contact is instantaneously at rest, and that's often a useful place to take moments about.

 

[PhizKid]

If I'm not mistaken, when you say the point to take the moment about that is not the same thing as the origin of the coordinate system is it?