Question:
A thin circular ring of 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. The wheel now rotates with an angular velocity
A thin circular ring of 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. The wheel now rotates with an angular velocity
Updated On: Jun 14, 2022
- $\frac{\omega M}{M+m}$
- $\frac{\omega( M -2 m )}{ M +2 m }$
- $\frac{\omega M}{M+2 m}$
- $\frac{\omega( M +2 m )}{ M }$
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The Correct Option is C
Solution and Explanation
Apply conservation of angular momentum.
$L _{ i } = L _{ f }$
$MR ^{2} \omega =( M +2 m ) R ^{2} \omega'$
$\omega'=\frac{ M \omega}{ M +2 m }$
$L _{ i } = L _{ f }$
$MR ^{2} \omega =( M +2 m ) R ^{2} \omega'$
$\omega'=\frac{ M \omega}{ M +2 m }$
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Concepts Used:
System of Particles and Rotational Motion
- The system of particles refers to the extended body which is considered a rigid body most of the time for simple or easy understanding. A rigid body is a body with a perfectly definite and unchangeable shape.
- The distance between the pair of particles in such a body does not replace or alter. Rotational motion can be described as the motion of a rigid body originates in such a manner that all of its particles move in a circle about an axis with a common angular velocity.
- The few common examples of rotational motion are the motion of the blade of a windmill and periodic motion.