HELP - ROTATIONAL INERTIA (no numbers given)

AI Thread Summary
The discussion focuses on calculating the mass and rotational inertia of a child's bowling ball compared to an adult's, given that the child's ball has half the radius. The relevant equations for rotational inertia are provided, specifically I=MR² for solid spheres. Participants clarify that since the densities are equal and the volumes differ, the masses of the two balls cannot be the same. The child’s ball's mass is reduced by a factor of 8, while its rotational inertia is reduced by a factor of 32. Understanding the relationship between radius, volume, and mass is crucial for solving the problem.
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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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