I was considering a Galilean problem on Quora of a ball moving at a
given velocity climbing a ramp of given height without slipping.
The question asked about its final velocity after the ascent.
This depends upon its kinetic energy, and how much is converted to
potential energy.
I considered two possibilities: solid sphere and hollow sphere.
I used two moments of inertia for these cases:2/5*m*r^2 & 3/5*m*r^2
These happen to be the values used by Dan MacIsaac in his 1996 video
tutorial at Buffalo, and by John Yelton at Oxford U., when upvoting a
similar calculation recently.
Then I happened on a list of Moments:
1) a sphere spinning on a central axis 2/5*m*r^2
2) a sphere rolling on a surface 7/5*m*r*2
And I was taken aback.
The academic sources seem to be juggling the measure for rotation to
make the lower value of Moment work, ignoring the axis of rotation
offset correction.
What am I missing?