Earth's Rotational Velocity: Find Linear Velocity

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SUMMARY

The discussion focuses on calculating the linear (or tangential) velocity of a point on the Earth's equator, considering the Earth as a rotating body around a stationary axis. The key equation involves understanding the relationship between rotational motion and linear velocity, specifically using the Earth's radius and the time it takes for one complete rotation (24 hours). The frame of reference is established as the Earth's center, which serves as the origin for this calculation.

PREREQUISITES
  • Understanding of rotational motion principles
  • Familiarity with linear velocity calculations
  • Knowledge of Earth's radius (approximately 6,371 kilometers)
  • Basic grasp of time measurement in hours and seconds
NEXT STEPS
  • Calculate linear velocity using the formula: v = 2πr/T, where r is the Earth's radius and T is the rotation period in seconds.
  • Explore the concept of frames of reference in physics.
  • Investigate the effects of Earth's rotation on various physical phenomena.
  • Learn about angular velocity and its relationship to linear velocity.
USEFUL FOR

Students studying physics, educators teaching rotational dynamics, and anyone interested in understanding the mechanics of Earth's motion.

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Homework Statement


Find the linear (or tangential) velocity of a point on the Earth's equator in the frame of reference about a stationary rotational axis as it spins over the course of one day.

Homework Equations

The Attempt at a Solution


I do not understand what the frame of reference is?? If a frame of reference isn't given, how do i find the linear velocity?
 
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It means taking the Earth's centre as the origin of a non-rotating frame.
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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