How Does Adding a Weight Affect the Center of Mass of a Wheel?

[lmf22]

A thin 6.0 kg wheel of radius 30 cm is weighted to one side by a 2.0 kg weight, small in size, placed 24 cm from the center of the wheel.
Calculate the position of the center of mass of the weighted wheel.

Here's what I have so far.
I set the origin as the center of the wheel.

Center of Mass = (6kg*0m)+(2kg*.24m)/8kg = 0.06m away from the center.

Is that correct?

 

[NateTG]

Looks good to me.

 

[wais]

Yes, your calculation for the position of the center of mass is correct. The center of mass of the weighted wheel is located 0.06m away from the center of the wheel, towards the side where the weight is placed. This means that the center of mass is not located at the exact center of the wheel, but slightly off to one side due to the added weight. This shift in the center of mass will affect the rotational inertia of the wheel and how it responds to external forces.