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

S. In summary, a student in a mechanics course is seeking help with a question about the effects of gravitational force on the rotation of the Earth. They have found a helpful thread on a forum discussing similar concepts and are looking for clarification on the relationship between acceleration due to gravity and centripetal acceleration.
  • #1
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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  • #3
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
 

1. What is weightlessness and how does it occur?

Weightlessness is the state of being without a sensation of weight or gravitational force acting upon an object. This occurs when an object is in free-fall or orbiting in space, where the gravitational force is counteracted by the centrifugal force of the object's motion.

2. How does weightlessness affect the human body?

Weightlessness can cause various physiological changes in the human body, such as a decrease in muscle mass, bone density, and cardiovascular function. It can also lead to fluid shifts, changes in spatial orientation, and changes in the immune system.

3. Can weightlessness be simulated on Earth?

Weightlessness can be simulated on Earth using parabolic flight maneuvers, where an aircraft follows a specific trajectory to create brief periods of weightlessness. It can also be simulated using neutral buoyancy tanks, where objects are submerged in water to create a similar effect.

4. How does weightlessness impact objects and materials?

Weightlessness can cause objects and materials to behave differently than they would on Earth. For example, fluids and gases can form spheres due to surface tension, and flames can burn in all directions. Objects may also experience microgravity, where they appear to be weightless but are still subject to small forces.

5. How do astronauts deal with the challenges of weightlessness in space?

Astronauts undergo rigorous training to prepare for the challenges of weightlessness in space. They also have specialized equipment, such as exercise machines, to help maintain their physical health. Additionally, they may use medication or special suits to help with fluid shifts and other physiological changes caused by weightlessness.

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