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

Options

A. `K = L^2//2 I`
B. `K = 2 l^2//I`
C. `K = L^2//I`
D. `K = sqrt(2) L^2//I`

Answer

A

Explanation

(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)`.