Two wheels having the same radius and mass rotate at the same angular velocity ((figure 1) ). one wheel is made with spokes so nearly all the mass is at the rim. the other is a solid disk. how do their rotational kinetic energies compare? a. the wheel with spokes has higher ke, but not twice as high. b. they are nearly the same. c. the solid wheel has higher ke, but not twice as high. d. the solid wheel has about twice the ke. e. the wheel with spokes has about twice the ke.

Explanation:

We have to consider how the location of the mass affects the moment of inertia.

For a solid cylinder, I = mR²

For a hollow cylinder, I = 1/2mR²

Where

I ist the moment of inertia,

m is their masses,

R is the radius of rotation.

Since they have the same mass and radius, it can be seen that a hollow cylinder has twice the moment of inertia as a solid cylinder of the same mass and radius.

We know that the rotational kinetic energy is proportional to the moment of inertia. From;

Rotational KE = 1/2IW²

Where W is the angular speed.

so that at the same angular speed, the wheel with the spokes will have about double the kinetic energy as the solid cylinder. Take note that some of the mass is in the spokes so the moment of inertia is not exactly double.