A uniform ring 1.3 m in diameter is pivoted at one point on its perimeter so tha

Question

A uniform ring 1.3 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. Axis 1) (a) If the ring is released from rest, what is its maximum angular velocity? rad/s Submit You currently have 0 submissions for this question. Only 2 submission are allowed You can make 2 more submissions for this question 2) (b) What minimum initial angular velocity must it be given if it is to rotate a full 360? rad/s Submit You currently have O submissions for this question. Only 2 submission are allowed. You can make 2 more submissions for this question

Explanation / Answer

R = D / 2 = 1.3 / 2 = 0.65 m

a) m g R = 1/2 I w2

m g R = 1/2 (2 M R2) w2

w = sqrt [g / R] = sqrt [9.8 / 0.65]

maximum angular velocity w = 3.88 rad/s

b) m g R + 1/2 I w2 = m g (2 R)

1/2 (2 M R2) w2 = m g R

wi = sqrt [g / R] = sqrt [9.8 / 0.65]

minimum initial angular velocity wi = 3.88 rad/s

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