Gravitation on three uniform spheres

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SUMMARY

The discussion centers on the gravitational acceleration experienced at the poles and equator of three uniform spheres with equal mass but different rotational periods: 16 hours for sphere A, 24 hours for sphere B, and 48 hours for sphere C. Despite having the same size and density, the net acceleration is influenced by centripetal acceleration, which is proportional to the radius and angular velocity. Sphere C, with the longest rotational period, exhibits the greatest net acceleration at both the poles and equator due to the lowest centripetal acceleration. Thus, the gravitational acceleration remains constant across all spheres, but the net acceleration varies based on rotational speed.

PREREQUISITES
  • Understanding of gravitational acceleration and centripetal acceleration
  • Familiarity with angular velocity and its effects on motion
  • Basic knowledge of uniform density and its implications in physics
  • Concept of net acceleration in rotating systems
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  • Research the mathematical relationship between angular velocity and centripetal acceleration
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  • Study the principles of uniform density in celestial bodies
  • Investigate the concept of net acceleration in various physical systems
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Students of physics, astrophysicists, and anyone interested in understanding the dynamics of rotating bodies and gravitational effects.

stunner5000pt
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Lets say we have three spheres all of uniform density and equal mass, However, sphere A has a rotational period of 16h, B has period of 24h and C has period of 48h.
So which one has the greatest acceleration (g value) at the poles and at the equator.
 
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I am sorely tempted to say that, since they all have the same size and density, they all have the same GRAVITATIONAL acceleration.

What you are asking about, however, is net acceleration.

A mass on a sphere of radius R, rotating with angular velocity ω, requires an inward (centripetal) acceleration of Rω2 just to stay on the surface. If you were to drop a mass at the surface of each of those spheres, the acceleration you would observe would be the "gravitational" acceleration (the same for all these spheres) minus the centripetal acceleration. Since that is proportional to R, you would observe the greatest acceleration on the sphere with least rotational speed: largest period- 48 hours.

I just noticed that you said "uniform density", not same density or same size. However, since uniform or non-uniform density is not really relevant to the problem, I going to assume you meant that the three spheres were all the same size and stick with my answer.
 
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