Small bead of mass 'm' moving with velocity 'v' gets threaded on a stationary semicircular ring of mass 'm' and radius 'r' kept on a horizontal table. The ring can freely rotate about its center o. The bead comes to rest relative to the ring. What would be the final angular velocity of the system?
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The final angular velocity of the system will be
Explanation :
Given data,
mass of bead = m
mass of ring = m
velocity of bead = v
radius of ring = r
Let the angular velocity of the system be ω
using the conservation of angular momentum about point o we get,
mvr = ω(mr² + mr²)
=> mvr = 2mωr²
=> v = 2ωr
=> ω =
Hence the final angular velocity of the system will be
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