Calculate the position of the center of mass of the weighted wheel

In summary, to calculate the position of the center of mass of the weighted wheel, we can use the formula (m1x1 + m2x2)/ (m1 + m2), where m1 and m2 are the masses and x1 and x2 are the distances from the origin. For part (b), we can use the formula for moment of inertia (I = Σmr^2) and consider the weight as a point mass to find its distance from the axis of rotation and compute the net moment of inertia.
  • #1
physicsss
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A thin 8.0 kg wheel of radius 28 cm is weighted to one side by a 5 kg weight, small in size, placed 10 cm from the center of the wheel.

(a) Calculate the position of the center of mass of the weighted wheel.

choosing the 8.0kg wheel to be on the origin, my cm is (8.0*0+5*0.1)/(8+5).


(b) Calculate the moment of inertia about an axis through its center of mass, perpendicular to its face.

How do I do that?
 
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  • #2
For part (b) you should know that the mass distribution consists of a continuous mass distribution plus a discrete mass. For a simple analysis, you can visualize the weight as a point mass and find its distance from the axis of rotation and compute the net moment of inertia (the sum).
 
  • #3
I don't really get what you are saying...
 

Related to Calculate the position of the center of mass of the weighted wheel

1. What is the center of mass?

The center of mass is a point in an object or system that represents the average position of all the mass in the object or system. It is the point at which the object or system can be balanced.

2. How is the center of mass calculated?

The center of mass is calculated by finding the weighted average of all the individual masses in the object or system. This is done by multiplying the mass of each component by its distance from a chosen reference point and then dividing the sum of these products by the total mass of the object or system.

3. Why is calculating the center of mass important?

Calculating the center of mass is important because it helps us understand how an object or system will behave when subjected to external forces. It also allows us to determine the stability and balance of an object or system.

4. What factors affect the position of the center of mass?

The position of the center of mass is affected by the distribution of mass within an object or system. The shape, size, and density of the object or system also play a role in determining the position of the center of mass.

5. Can the center of mass be outside of the object or system?

Yes, the center of mass can be outside of the object or system if the mass is distributed unevenly or if there are external forces acting on the object or system. In some cases, the center of mass may even be located in empty space outside of the object or system.

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