Simple Physics question about rotational inertia

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SUMMARY

The discussion focuses on the physics of rotational inertia, specifically comparing a child's bowling ball to an adult's. The child's ball has two-thirds the radius of the adult ball, leading to a mass reduction factor of 1/3, as both balls are made of the same material. The rotational inertia of the child's ball is calculated using the formula I = 1/2 MR^2, resulting in a reduction factor of 1/3 compared to the adult ball. This analysis is crucial for understanding the relationship between radius, mass, and rotational inertia in spherical objects.

PREREQUISITES
  • Understanding of rotational inertia and its formula, I = 1/2 MR^2
  • Knowledge of the volume formula for a sphere
  • Basic principles of mass and density in physics
  • Familiarity with scaling laws in physics
NEXT STEPS
  • Research the derivation of the rotational inertia formula for different shapes
  • Explore the relationship between radius and volume in spherical objects
  • Study the effects of material density on mass and inertia
  • Investigate real-world applications of rotational inertia in sports equipment
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Students studying physics, particularly those focusing on mechanics and rotational dynamics, as well as educators looking for examples of mass and inertia relationships in practical scenarios.

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Homework Statement


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

(b) By what factor is the rotational inertia of the child's ball reduced compared with the adult ball?


Homework Equations



1/2 MR^2 , i believe

The Attempt at a Solution


I thought that the answer to part is is just 1/3 but my online assignment is accepting it as the correct answer.
part b would then be 2/3 squared * 1/2 = 1/3
 
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(a) What is the formula for the volume of a sphere?
 

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