What is its rotational kinetic energy?

[Elleboys]

Homework Statement

A 240g ball and a 570g ball are connected by a 48.0-cm-long massless, rigid rod. The structure rotates about its center of mass at 110 rpm.

Homework Equations

KE = Iω^2
I = 1/12(mr^2)

The Attempt at a Solution

Since it has two masses and two different radius, I was not sure with what I should've done.

 

[Curious3141]

Homework Statement

A 240g ball and a 570g ball are connected by a 48.0-cm-long massless, rigid rod. The structure rotates about its center of mass at 110 rpm.

Homework Equations

KE = Iω^2
I = 1/12(mr^2)

The Attempt at a Solution

Since it has two masses and two different radius, I was not sure with what I should've done.

Where did your formula for the moment of inertia come from? That doesn't look like the moment of inertia of a solid sphere (ball) to me.

To do this problem, you need the radius of each ball. Are you given this?

The first step is to find the common centre of mass (COM) of the system. Do you know how to do that?

The next step is to calculate the moment of inertia of the system about that common COM. This can be done by summing up the moments of each ball. Remember to use the right formula and remember the parallel axis theorem.

The final step to find the rotational KE is trivial. But you should note that even your formula for rotational KE is wrong (missing a factor of 0.5).

 

[Elleboys]

Where did your formula for the moment of inertia come from? That doesn't look like the moment of inertia of a solid sphere (ball) to me.

To do this problem, you need the radius of each ball. Are you given this?

The first step is to find the common centre of mass (COM) of the system. Do you know how to do that?

The next step is to calculate the moment of inertia of the system about that common COM. This can be done by summing up the moments of each ball. Remember to use the right formula and remember the parallel axis theorem.

The final step to find the rotational KE is trivial. But you should note that even your formula for rotational KE is wrong (missing a factor of 0.5).

OHHHHH I see
And yes I put wrong formula for I.
So I believe that I need to find a center of mass, get moment of inertia of each particle about that COM, add them up and it will give me net moment of inertia.
And by using KE = Iω^2, I can get the answer.
Am I on the right track?

 

[contrivance]

And by using KE = Iω^2, I can get the answer.
Am I on the right track?

You still need to add the 0.5 on front of your formula for KE like Curious3141 said. KE = 0.5Iω^2

 

[Curious3141]

OHHHHH I see
And yes I put wrong formula for I.
So I believe that I need to find a center of mass, get moment of inertia of each particle about that COM, add them up and it will give me net moment of inertia.
And by using KE = Iω^2, I can get the answer.
Am I on the right track?

Yes, you're on the right track (except that $K = \frac{1}{2}I\omega^2$). Work through it systematically.