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!
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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