Question

Show that the kinetic energy of a rotating body about a given axix is equal to 1/2Lw where L is angular momentum and w is is angular velocity.​

Answer 1

Answer:

The rotational kinetic energy of a body is given by E= 1/2 Iw2, where w is angular velocity of the body. UseKinetic energy increases quadratically with speed. ... Rotational kinetic energy = ½ moment of inertia * (angular speed)2. ... Each step corresponds to a time interval of (1/30) s.

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Answer 2

Answer:

The kinetic energy of the rotating body about a given axis is equal to $\frac{1}{2}L\omega$.

Explanation:

The kinetic energy of the rotating body about an axis is given as,

$K=\frac{1}{2} I\omega^2$           (1)

Where,

k

K=kinetic energy of the rotating body

I=moment of inertia of the rotation of a given body about a particular axis

ω=angular velocity of the rotating body

From the conservation of angular momentum we have,

$L=I\omega$             (2)

Where,

L=angular momentum of the rotating body

By substituting equation (2) in equation (1) we get;

$K=\frac{1}{2} I\omega\times \omega$

$K=\frac{1}{2}L\omega$

Hence, the kinetic energy of a rotating body about a given axis is equal to $\frac{1}{2}L\omega$.