How Long Would a Day Be If the Earth Rotated Fast Enough for Equatorial Objects to Be Weightless?

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SUMMARY

The discussion centers on the theoretical scenario of Earth rotating at a speed that would render objects at the Equator weightless. This condition occurs when the centripetal acceleration equals the gravitational acceleration. Specifically, the required rotational speed can be calculated using the formula for centripetal acceleration, which is derived from Newton's laws of motion. The conversation also references the concept of satellites maintaining orbit just above the Earth's surface, emphasizing the relationship between gravitational and centrifugal forces.

PREREQUISITES
  • Understanding of Newton's laws of motion
  • Familiarity with centripetal acceleration
  • Basic knowledge of gravitational forces
  • Concept of non-inertial reference frames
NEXT STEPS
  • Research the formula for centripetal acceleration in detail
  • Explore the effects of varying rotational speeds on gravitational forces
  • Study satellite motion and orbital mechanics
  • Investigate the implications of non-inertial frames in physics
USEFUL FOR

Students in physics or mechanics courses, educators teaching gravitational concepts, and anyone interested in the dynamics of rotational motion and its effects on weightlessness.

Theelectricchild
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Hi everyone I am a student in a mechanics course.

We just had a brief intro into gravitation and Newtons synthesis and I was wondering how I can solve this question...

How long would a day be if the Earth were rotating so fast that objects at the Equator were weightless?

The reading on the section is short, thanks for your help.
 
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The same question in different words:

How fast would a satellite have to travel to stay in orbit just a few centimeters above the Earth's surface?

It's all a matter of acceleration due to gravity matching centripetal acceleration--or, in my non-inertial frame, force of gravity matching centrifugal force.

P
 

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