Express h in Terms of r and theta: Rotational Physics

In summary, the question asks to express the height h in terms of the radius r and angle theta for a rotating disc released from rest with a block causing it to rotate after a time t, and the answer is simply h = r*theta.
  • #1
scifan
2
0
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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  • #2
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!
 
  • #3


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?
 
  • #5


Your answer is correct and in terms of r and theta. The g and t terms are constants and do not affect the relationship between h, r, and theta. To express h in terms of only r and theta, you can simply replace g and t with their numerical values or leave them as variables. The important thing is that the equation shows the relationship between h, r, and theta.
 

1. What is the formula for expressing h in terms of r and theta in rotational physics?

The formula for expressing h in terms of r and theta in rotational physics is h = r * sin(theta), where r is the radius and theta is the angle of rotation.

2. How is the height of an object related to its radius and angle of rotation in rotational physics?

In rotational physics, the height of an object is directly proportional to its radius and the sine of the angle of rotation. This means that as the radius or angle of rotation increases, the height also increases.

3. Can h be negative when expressing it in terms of r and theta in rotational physics?

Yes, h can be negative when expressing it in terms of r and theta in rotational physics. This occurs when the angle of rotation is in the third or fourth quadrant, where the sine function is negative.

4. How do you use the formula for expressing h in terms of r and theta to solve rotational physics problems?

To solve rotational physics problems using the formula for expressing h in terms of r and theta, you first need to have the values for r and theta. Then, simply plug these values into the formula and solve for h.

5. Can the formula for expressing h in terms of r and theta be applied to any object in rotational motion?

Yes, the formula for expressing h in terms of r and theta can be applied to any object in rotational motion, as long as the object has a circular shape and is rotating around a fixed axis.

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