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maniacp08
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Rotation -- Anuglar speed
A uniform ring 2.2 M in diameter is pivoted at one point on its perimeter so that it is free to rotate about a horizontal axis. Initially, the line joining the support point and center is horizontal.
(a) If the ring is released from rest, what is its maximum angular velocity?
rad/s
(b) What minimum initial angular velocity must it be given if it is to rotate a full 360°?
rad/s
What I did:
I used energy of conservation on this.
The maximum velocity would be when the potential energy is at 0 since it is all converted into kinetic energy.
R = 1.1m
Moment of inertia for the ring is MR^2
Moment of the inertia of the pivot = 1/2 MR^2 + MR^2 = 3MR^2/2
Ui + Ki = Uf + Kf
MgR + 0 = 0 + 1/2 (3MR^2/2)*omega ^2
MgR = 1/2 (3MR^2/2)*omega ^2
omega = square root of 2(g/3R)
V = omega * R = square root of 2(gR/3R)
It is at the bottom when it is 2R so
V= omega * 2R = square root of 4(gR/3)
What did I do wrong?
For Part B:
To find the minimum velocity to do a full 360, can I do this:
Ui + Ki = Uf + kf
MgR + 0 = 2MgR + 1/2 (3MR^2/2)*omega ^2
and solve for velocity as I did above?
A uniform ring 2.2 M in diameter is pivoted at one point on its perimeter so that it is free to rotate about a horizontal axis. Initially, the line joining the support point and center is horizontal.
(a) If the ring is released from rest, what is its maximum angular velocity?
rad/s
(b) What minimum initial angular velocity must it be given if it is to rotate a full 360°?
rad/s
What I did:
I used energy of conservation on this.
The maximum velocity would be when the potential energy is at 0 since it is all converted into kinetic energy.
R = 1.1m
Moment of inertia for the ring is MR^2
Moment of the inertia of the pivot = 1/2 MR^2 + MR^2 = 3MR^2/2
Ui + Ki = Uf + Kf
MgR + 0 = 0 + 1/2 (3MR^2/2)*omega ^2
MgR = 1/2 (3MR^2/2)*omega ^2
omega = square root of 2(g/3R)
V = omega * R = square root of 2(gR/3R)
It is at the bottom when it is 2R so
V= omega * 2R = square root of 4(gR/3)
What did I do wrong?
For Part B:
To find the minimum velocity to do a full 360, can I do this:
Ui + Ki = Uf + kf
MgR + 0 = 2MgR + 1/2 (3MR^2/2)*omega ^2
and solve for velocity as I did above?
Last edited: