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The kinetic energy of an object rotating...

The kinetic energy of an object rotating about a fixed axis with angular momentum `L = I omega` can be written as.

A

`K = L^2//2 I`

B

`K = 2 l^2//I`

C

`K = L^2//I`

D

`K = sqrt(2) L^2//I`

Text Solution

Verified by Experts

The correct Answer is:
A
(a) We begin with `K = (1)/(2) I omega^2`
And multiply the right-hand side by `(I)/(I)` :
`K = (1)/(2)I omega^2 = (1)/(2) (I^2 omega^2)/(I)`
Substituting `L = I omega` then gives
`K = (1)/(2) I omega^2 = (1)/(2) (I^2 omega^2)/(I) = (L^2)/(2 I)`.
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Knowledge Check

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