Question

Find the kinetic energy K of a particle of mass m, moving in a circular path, if L is its angular momentum and I is its moment of inertia about the center of the circle. Express your answer in terms of the variables L and I.

Answer 1

k=
`(1)/(2)L^2/I`

Step-by-step explanation:

we know that:

L = IW

where L is the angular momentum, I the moment of inertia and W is the angular velocity.

and Also we know that:

k=
`(1)/(2)IW^2`

Now, we solve the first equation for W and get:

W = L/I

Replacing W on the first equation we get:

`k=(1)/(2)I((L)/(I))^(2) =(1)/(2) (L^(2))/(I)`