Express h in Terms of r and theta: Rotational Physics

AI Thread Summary
The discussion centers on expressing the height h in terms of the radius r and the angle theta for a disc rotating due to a falling block. Initially, the user attempts to derive h using energy conservation, but others clarify that the problem is fundamentally geometric. The correct relationship is established as h = r*theta, reflecting the winding constraint of the string around the disc's hub. This geometric approach simplifies the problem, eliminating the need for gravitational acceleration and time in the final expression. The consensus emphasizes the importance of recognizing the geometric nature of the relationship in rotational physics.
scifan
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So the question is this:

A disc is released from rest. A block is causing it to rotate. After a time t the block has fallen a height h and the disc has rotated through an angle theta. (in rad)
Express h in terms of r (the radius of the part of the hub around which the string is wound) and theta.

I came up with this answer:

PE lost = KE gained
mgh = (1/2)mv^2 + (1/2)I(omega)^2
mgh = (1/2)m(r*omega)^2 + (1/2)*(mr^2)omega^2
gh = (1/2)r^2*omega^2 + (1/2)omega^2*r^2
gh = omega^2*r^2
omega = d(theta)/dt
subs for omega and solve for h: h = (r^2*theta^2)/(t^2*g)

The question asks me to express h in terms of r and theta but my answer has g and t in it. Any help?

Thanks in advance!
 
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welcome to pf!

hi scifan! welcome to pf! :smile:

(have a theta: θ and try using the X2 icon just above the Reply box :wink:)
scifan said:
A disc is released from rest. A block is causing it to rotate. After a time t the block has fallen a height h and the disc has rotated through an angle theta. (in rad)
Express h in terms of r (the radius of the part of the hub around which the string is wound) and theta.

read the question! :rolleyes:

energy has nothing to do with it …

this is just geometry!​
 


tiny-tim said:
hi scifan! welcome to pf! :smile:

(have a theta: θ and try using the X2 icon just above the Reply box :wink:)


read the question! :rolleyes:

energy has nothing to do with it …

this is just geometry!​


Would that be correct if I say h = r*theta then?
 

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