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A disc is rotating about vertical axis O...

A disc is rotating about vertical axis OA, which is tangent to the circumference and perpendicular to the plane of disc. Its rotational energy is given as E. Find the time period of rotation.

Text Solution

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Moment of inertia about `OA = (1)/(2) mR^(2) + mR^(2) = (3)/(2) mR^(2)`
`E = (1)/(2) I_(OA) omega^(2) = (1)/(2) (3)/(2) mR^(2) omega^(2)`
`(4)/(3) (E)/(mR^(2)) = omega^(2)`
`rArr" "omega = sqrt((4)/(3) (E)/(mR^(2)))`
Time period `= (2pi)/(omega) = 2pi sqrt((3mR^(2))/(4E)) = pi sqrt((3mR^(2))/(E))`
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