Question

Express the kinetic energy of a rotating body in term’s of its angular momentum.

Answer 1

Explanation:

Rotational kinetic energy can be expressed as: Erotational=12Iω2 E rotational = 1 2 I ω 2 where ω is the angular velocity and I is the moment of inertia around the axis of rotation. ... The instantaneous power of an angularly accelerating body is the torque times the angular velocity: P=τω P = τ ω .

Answer 2

GIVEN :

A Rotating body.

TO FIND

To express Kinetic energy in terms of angular momentum

SOLUTION:

The rotational kinetic or angular kinetic energy is the the kinetic energy in a rotating body.

So, kinetic energy of a body with momemt of inertia I rotating with an angular velocity ω, is given as -

$E=\frac{1}{2} Iω^{2}$          (eq. 1)

Now, we know that the angular momentum L,  is represented as -

L = I ω.           (eq. 2 )

Putting the value of L in formula for kinetic energy we get,

$E = \frac{1}{2} Lω$

Hence, the rotational kinetic energy is directly proportional to it's angular momentum

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