Question

A thin circular ring if mass M and radius R is rotating about its axis with a constant angular velocity omega. Two objects each of mass m, are attached gently to the opposite ends of a diameter of the ring. Find the new angular velocity of the ring

Answer 1

The new angular velocity of the ring is W2 = Mw/M + 2m

Explanation:

• We are given the mass to be M and the radius to be R.
• The mass of the objects attached is m
• We use the law of conservation of angular momentum which says that:

Initial angular momentum= Final angular momentum

L1w1 = L2w2

W1 is the initial angular velocity and w2 is the new angular velocity

Here,

L1 = MR^2

L2 = MR^2 + 2mMR^2

(2m because 2 objects of mass m are attached)

W1 =  ω

• Then we get  

W2 = l1 ω/ L2

W2 = MR^2  ω/MR^2  + 2mR^2

W2 = Mw/M + 2m

Thus the new angular velocity of the ring is W2 = Mw/M + 2m

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Answer 2

Answer:

Explanation:

please check the attachment