- #1

Leo Liu

- 353

- 149

- Homework Statement:
- A thin hoop of mass M and radius R is suspended from a string through a point on the rim of the hoop. If the support is turned with high angular velocity ω, the hoop will spin as shown, with its plane nearly horizontal and its center nearly on the axis of the support. The string makes angle α with the vertical. (a) Find, approximately, the small angle β between the plane of the hoop and the horizontal. Assume that the center of mass is at rest.

- Relevant Equations:
- .

Problem (

Solution:

My questions:

1. The official solution gives no information about the point at which the torque is measured. I thought it was the CM of the hoop, but the torque should be ##\tau=RT\cos(\alpha-\beta)##; the angle was given by a geometric proof. I would like to know where the torque is calculated in the solution.

2. Why is the rate of change of momentum ##L_s\omega_s## rather than ##L_s\dot\theta_y## (see the diagram in blue & red), and why is this term multiplied by ##\sin\beta##? Does this have something to do with the choice of coordinate?

Thank you.

**a only**):Solution:

My questions:

1. The official solution gives no information about the point at which the torque is measured. I thought it was the CM of the hoop, but the torque should be ##\tau=RT\cos(\alpha-\beta)##; the angle was given by a geometric proof. I would like to know where the torque is calculated in the solution.

2. Why is the rate of change of momentum ##L_s\omega_s## rather than ##L_s\dot\theta_y## (see the diagram in blue & red), and why is this term multiplied by ##\sin\beta##? Does this have something to do with the choice of coordinate?

Thank you.