I don't get why this is the same?

[flyingpig]

I don't get why this is the same??

Homework Statement

[PLAIN]http://img577.imageshack.us/img577/1213/33472409.jpg

[PLAIN]http://img695.imageshack.us/img695/2961/93055936.jpg

SOLUTIONS

[PLAIN]http://img213.imageshack.us/img213/1912/64111316.jpg

[PLAIN]http://img804.imageshack.us/img804/2032/78965826.jpg

Here is my first question, why did they have two different 'h's? I don't understand why they substitute the H in part a into b, isn't that different? The H is without friction and the H in part b is the one with friction.

Now for part c

[PLAIN]http://img152.imageshack.us/img152/2179/28718730.jpg

When I first did the problem I didn't know if v(0) was the speed for the center of mass or tangential speed, but it seems like it is tangential speed. My question is, how exactly do we know it is the tangential speed and not the center of mass?

 

[Gear300]

For the first question, H is the maximum height without friction, whereas h is the maximum height with friction. The problem asked to give h in terms of H.

For the second question, v₀ is the center of mass speed as well as the tangential speed. When an object rolls across a surface in the way specified in the question, the translational speed equates with the tangential speed (this is because R happens to be both the distance of the center of mass above the point of contact with the surface and the radius of the object about its center of mass).

 

[flyingpig]

For the first question, H is the maximum height without friction, whereas h is the maximum height with friction. The problem asked to give h in terms of H.

Somewhat satisfied with that answer, I just need a tiny bit of more convincing.

For the second question, v₀ is the center of mass speed as well as the tangential speed. When an object rolls across a surface in the way specified in the question, the translational speed equates with the tangential speed (this is because R happens to be both the distance of the center of mass above the point of contact with the surface and the radius of the object about its center of mass).

Yes, so doesn't that mean the top actually is 2v₀ instead?

 

[Gear300]

Yes, so doesn't that mean the top actually is 2v₀ instead?

Yup, you're right...I didn't present my answer clearly; the two don't have the same translational speed. The equivalence I gave is between two different reference frames. Since the moment of inertia they used is centered around the center of mass, you're describing the tangential speed relative to the center of mass, which would be v₀. If you were to look at it in terms of 2v₀, then the rotation would occur around the point of contact with the surface, which would end up complicating the expression for the moment of inertia.

 

[flyingpig]

Yup, you're right...I didn't present my answer clearly; the two don't have the same translational speed. The equivalence I gave is between two different reference frames. Since the moment of inertia they used is centered around the center of mass, you're describing the tangential speed relative to the center of mass, which would be v₀. If you were to look at it in terms of 2v₀, then the rotation would occur around the point of contact with the surface, which would end up complicating the expression for the moment of inertia.

Could you dumb that down a bit...?

 

[Doc Al]

When I first did the problem I didn't know if v(0) was the speed for the center of mass or tangential speed, but it seems like it is tangential speed. My question is, how exactly do we know it is the tangential speed and not the center of mass?

v₀ is the initial speed of the center of mass.