Question

Two disks with the same rotational inertia i are spinning about the same frictionless shaft, with the same angular speed ω, but with opposite angular velocities ~ω and −~ω. what is the total rotational kinetic energy kr of this system of two disks? 1. 1 2 i ω 2 2. zero 3. none of these

Answer 1

Answer:

3. none of these

Explanation:

The rotational kinetic energy of an object is given by:

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

where

I is the moment of inertia

$\omega$ is the angular speed

In this problem, we have two objects rotating, so the total rotational kinetic energy will be the sum of the rotational energies of each object.

For disk 1:

$K_1 = \frac{1}{2}I (\omega)^2 = \frac{1}{2}I\omega^2$

For disk 2:

$K_2 = \frac{1}{2}I(-\omega)^2 = \frac{1}{2}I\omega^2$

so the total energy is

$K=K_1 + K_2 = \frac{1}{2}I\omega^2 + \frac{1}{2}I\omega^2 = I\omega^2$

So, none of the options is correct.