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System of Particles and Rotational Motion

Angular displacement, angular velocity, angular acceleration

A uniform circular disc of mass 50 {~kg} and radius 0.4 {~m} i

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Solving time: 3 mins

A uniform circular disc of mass $50 kg$ and radius $0.4 m$ is rotating with an angular velocity of $10 rad / s$ about its own axis, which is vertical. Two uniform circular rings, each of mass $6.25 kg$ and radius $0.2$ $m$ , are gently placed symmetrically on the disc in such a manner that they are touching each other along the axis of the disc and are horizontal. Assume that the friction is large enough such that the rings are at rest relative to the disc and the system rotates about the original axis. The new angular velocity (in rad $s^{- 1}$ ) of the system is ..................

Uploaded: 2022-10-17T15:28:05.000Z
Duration: 5 min

Views: 5,688 students

Updated on: Oct 17, 2022

Book:

Mechanics Volume 2 (DC Pandey)

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A uniform circular disc of mass

50 kg

and radius

0.4 m

is rotating with an angular velocity of

10 rad / s

about its own axis, which is vertical. Two uniform circular rings, each of mass

6.25 kg

and radius

0.2

m

, are gently placed symmetrically on the disc in such a manner that they are touching each other along the axis of the disc and are horizontal. Assume that the friction is large enough such that the rings are at rest relative to the disc and the system rotates about the original axis. The new angular velocity (in rad

s^{- 1}

) of the system is ..................

14 mins ago

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14 mins ago

Text solutionVerified

∴ ω_{2} = (\frac{l _{1}}{I _{2}}) ω_{1} = [\frac{\frac{1}{2} M R ^{2}}{\frac{1}{2} M R ^{2} + 2 ( m r ^{2} )}] ω_{1} = [\frac{50 ( 0.4 ) ^{2}}{50 ( 0.4 ) ^{2} + 8 \times ( 6.25 ) \times ( 0.2 ) ^{2}}] (10 = 8 rad / s

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Question Text	A uniform circular disc of mass $50 kg$ and radius $0.4 m$ is rotating with an angular velocity of $10 rad / s$ about its own axis, which is vertical. Two uniform circular rings, each of mass $6.25 kg$ and radius $0.2$ $m$ , are gently placed symmetrically on the disc in such a manner that they are touching each other along the axis of the disc and are horizontal. Assume that the friction is large enough such that the rings are at rest relative to the disc and the system rotates about the original axis. The new angular velocity (in rad $s^{- 1}$ ) of the system is ..................
Updated On	Oct 17, 2022
Topic	System of Particles and Rotational Motion
Subject	Physics
Class	Class 11
Answer Type	Text solution:1 Video solution: 2
Upvotes	254
Avg. Video Duration	4 min

Text solutionVerified

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