Calculating Moment of Inertia for a Thin Spherical Shell

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In summary, the conversation pertains to finding the moment of inertia of a thin spherical shell with a mass of 60.0 g and a diameter of 6.98 cm. The correct formula for moment of inertia is 2/5Mr^2, and after converting the units and plugging in the numbers, the answer should be 2.92 *10^-5 kg*m^2. However, the person has made multiple attempts and received incorrect answers. They eventually found the correct answer on another site.
  • #1
tak08810
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Ok this problem is really really ticking me off because it seems so damn simple.

"A rubber ball has a mass of 60.0 g and a diameter of 6.98 cm. Find the moment of inertia about its diameter. Model the ball as a thin spherical shell."

Ok so moment of interia for a sphere shaped object is 2/5Mr^2 correct? So I convert grams to kg, cm to meters, plug the numbers in (radius = 0.0349 m) and get 2.92 *10^-5 kg*m^2. But this is wrong? I don't understand what I'm doing wrong. I assume I'm looking at this problem in completely the wrong way. Here is the list of attempts I've put in:

Submission # Try Submitted Answer
1 Incorrect. (Try 1) 2.92 *10^-5 kg*m^2
2 Incorrect. (Try 2) 1.17 *10^-4 kg*m^2
3 Incorrect. (Try 3) 7.30 *10^-5 kg*m^2
4 Incorrect. (Try 4) 2.92 *10^-4 kg*m^2
5 Incorrect. (Try 5) 2.93 *10^-5 kg*m^2
6 Incorrect. (Try 6) 2.91 *10^-5 kg*m^2
7 Submission not graded. Use more digits. 2.9 *10^-5 kg*m^2
8 Submission not graded. Use fewer digits. 1.1692896 *10^-4 kg*m^2
9 Incorrect. (Try 7) 1.1692 *10^-4 kg*m^2
10 Incorrect. (Try 8) 0.000 kg*m^2
11 Incorrect. (Try 9) 0.000292 kg*m^2
12 Incorrect. (Try 10) 0.000117 kg*m^2
13 Incorrect. (Try 11) 0.0004188 kg*m^2
14 Incorrect. (Try 12) 0.004188 kg*m^2
15 Incorrect. (Try 13) 0.000251 kg*m^2
16 Incorrect. (Try 14) 0.000251 g*m^2
17 Incorrect. (Try 15) 2.92 *10^-5 kg*m^2
 
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  • #2
NVM I got the answer from another site. Thanks anyways!
 

1. What is moment of inertia?

Moment of inertia is a measure of an object's resistance to rotational motion. It is a property that depends on the object's mass and the distribution of that mass around an axis of rotation.

2. How is moment of inertia calculated?

The moment of inertia of an object is calculated by taking the sum of the mass of each individual particle in the object multiplied by the square of its distance from the axis of rotation.

3. What are the units of moment of inertia?

The units of moment of inertia depend on the units of mass and distance used in the calculation. In the SI system, the units are kilogram meter squared (kg m^2)

4. What is the importance of moment of inertia in physics?

Moment of inertia is an important concept in rotational dynamics, as it helps us understand how objects move and rotate in response to external forces. It also plays a crucial role in the conservation of angular momentum.

5. How does the moment of inertia change with the shape of an object?

The moment of inertia is affected by the distribution of an object's mass, so the shape of an object can greatly influence its moment of inertia. Objects with more mass concentrated near the axis of rotation will have a smaller moment of inertia, while objects with more mass farther from the axis will have a larger moment of inertia.

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