Calculating Position of CM & Moment of Inertia for Weighted Wheel

In summary, the conversation discusses the calculation of the position of the center of mass and the moment of inertia of a weighted wheel. The center of mass is found to be 3.125 cm from the center of the wheel, and the parallel axis theorem is used to calculate the moment of inertia about an axis through its center. The conversation also mentions the lack of proper teaching of physics in the class.
  • #1
Stryder_SW
23
0

Homework Statement


A thin 7.0 kg wheel of radius 32 cm is weighted to one side by a 1.0 kg weight, small in size, placed 25 cm from the center of the wheel.

(a) Calculate the position of the center of mass of the weighted wheel.
*edit* found the CM, its 3.125cm from the center *edit*
(b) Calculate the moment of inertia about an axis through its CM, perpendicular to its face.
*edit*SOLVED*edit*

2. The attempt at a solution
*edit*I realize I need to use the parallel axis theorem on part b, but I don't really understand how to apply it.*edit*
 
Last edited:
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  • #2
Hi Stryder_SW! :smile:
Stryder_SW said:
(b) Calculate the moment of inertia about an axis through its CM, perpendicular to its face.
…
a nudge in the right direction would be greatly appreciated.

nudge nudge …

from the PF Library … Parallel axis theorem: the moment of inertia of a body about an axis is IC + md2

where m is the mass, d is the distance from that axis to the centre of mass, and IC is the Moment of Inertia about the parallel axis through the centre of mass.

:wink: :wink:​
 
  • #3
Has your class talked about the parallel axis theorem? You have here two bodies, and it is not difficult to find the MMOI for each of them separately with respect to their own CM. Now you need to transfer that MMOI to their common CM and add them.
 
  • #4
No, unfortunately my class fails at teaching physics. We tend to skip over these important theorems that make our lives so much easier.
 
  • #5
I realize I need to use the parallel axis theorem, but I'm having a hard time applying it.
 

1. How do you calculate the position of the center of mass (CM) for a weighted wheel?

To calculate the position of the CM for a weighted wheel, you will need to know the mass and distribution of the weight around the wheel. The position of the CM can be found using the formula: CM = (m1r1 + m2r2 + ... + mnrn) / (m1 + m2 + ... + mn), where m represents the mass of each section and r represents the distance from that section to the axis of rotation.

2. What is the moment of inertia for a weighted wheel?

The moment of inertia for a weighted wheel is a measure of its resistance to rotational motion. It is calculated by summing up the products of each mass element and its distance squared from the axis of rotation. The formula for moment of inertia is I = Σmiri², where m represents the mass of each element and r represents the distance from the axis of rotation.

3. How does the distribution of weight on a wheel affect its moment of inertia?

The distribution of weight on a wheel directly affects its moment of inertia. A wheel with more weight distributed towards the outer edge will have a larger moment of inertia than a wheel with weight concentrated towards the center. This is because the farther the mass is from the axis of rotation, the more force is required to change its rotational motion.

4. Can the position of the CM and moment of inertia change for a weighted wheel?

Yes, the position of the CM and moment of inertia can change for a weighted wheel if the distribution of weight changes. For example, if weight is added or removed from one side of the wheel, the position of the CM will shift and the moment of inertia will also change. However, the total mass of the wheel will remain the same.

5. How can the calculated position of the CM and moment of inertia be used in practical applications?

The position of the CM and moment of inertia for a weighted wheel are important factors in determining its stability, balance, and performance. In practical applications, this information can be used to design more efficient and stable wheels for vehicles, machines, and other rotating objects. It can also be used to calculate the necessary force and torque required to accelerate or decelerate the wheel.

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