HELP - ROTATIONAL INERTIA (no numbers given)

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Homework Help Overview

The discussion revolves around the concept of rotational inertia in the context of comparing a child's bowling ball to an adult's bowling ball, focusing on how changes in radius affect mass and rotational inertia. The problem involves understanding the relationship between density, volume, and mass for spheres made of the same material.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss setting densities equal to analyze how mass varies with radius. There is a suggestion to calculate the volumes of the spheres first to understand the differences in mass and rotational inertia. Questions arise about the implications of equal densities on mass calculations.

Discussion Status

The discussion is active, with participants exploring different interpretations of the problem. Some guidance has been offered regarding the need to find volumes, and there is an ongoing examination of how mass is affected by the differing radii of the bowling balls.

Contextual Notes

Participants note that the problem does not provide numerical values and that the relationship between mass and volume is central to the discussion. The assumption that the balls are made of the same material is also a key point of consideration.

Quarkn
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Homework Statement


A bowling ball made for a child has half the radius of an adult bowling ball. They are made of the same material (and therefore have the same mass per unit volume). By what factor is a) mass and b) rotational inertia if the child's ball reduced compared with the adult ball?


Homework Equations


I=MR²
(sphere) I=(2/5)MR²


The Attempt at a Solution


I only got to: R(adult) = (1/2)R (child).

PS. the answers to a) reduced by a factor of 8 and b)reduced by a factor of 32
 
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Set the two densities equal to each other, and then examine how the masses vary (since the radius of the child's bowling ball differs from the adult's). Based on this, you should have enough information to determine its moment of inertia.
 
physicsvalk said:
Set the two densities equal to each other, and then examine how the masses vary (since the radius of the child's bowling ball differs from the adult's). Based on this, you should have enough information to determine its moment of inertia.

So would you find the volume of each spheres first?

And if i set the two densities equal, wouldn't the masses just cancel?

ex. D=M/V, M/v=M/V ?
 
Yes, you would need to find the volumes.

The densities are said to be equal and the volumes differ, therefore, the masses can't be the same.
 

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