Express h in Terms of r and theta: Rotational Physics

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SUMMARY

The discussion centers on expressing the height h of a falling block in terms of the radius r of a disc and the angle theta through which the disc rotates. The initial approach involved energy conservation principles, equating potential energy lost to kinetic energy gained. However, the correct relationship is derived from geometric constraints, leading to the conclusion that h = r * theta. This relationship is recognized as the standard "winding constraint" in rotational physics.

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  • Knowledge of angular displacement and its relationship to linear displacement
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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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