Question

Derive an expression for the kinetic energy of a body rotating with uniform angular

speed.​

Answer 1

Answer:

The kinetic energy of a body rotating with uniform angular speed is given by the formula K = (1/2) I ω², where I is the moment of inertia of the body and ω is the angular velocity of the body.

Explanation:

The kinetic energy of a rotating body is given by the formula:

K = (1/2) I ω²

Where K is the kinetic energy of the body, I is the moment of inertia of the body, and ω is the angular velocity of the body.

If the body is rotating with uniform angular speed, then the angular velocity ω is constant. Therefore, we can simplify the above formula as:

K = (1/2) I ω²

K = (1/2) I (θ/t)²

where θ is the angle through which the body rotates in time t.

Since the body is rotating with uniform angular speed, we can express θ as θ = ωt. Substituting this in the above equation, we get:

K = (1/2) I (ωt/t)²

K = (1/2) I ω²

Therefore, the kinetic energy of a body rotating with uniform angular speed is given by the formula K = (1/2) I ω², where I is the moment of inertia of the body and ω is the angular velocity of the body.

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