Circular Motion of Newton's Laws

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SUMMARY

The discussion centers on calculating the new rotational period of Earth required for an object at the equator to experience zero apparent weight, utilizing the formula T = 2π√(R/g). Participants seek clarification on determining the radius (R) and the implications of increased rotational speed. The key takeaway is that the apparent weight becomes zero when the normal force is nullified, necessitating precise calculations of both period and speed increase factors.

PREREQUISITES
  • Understanding of Newton's Laws of Motion
  • Familiarity with circular motion concepts
  • Knowledge of gravitational acceleration (g)
  • Ability to manipulate mathematical formulas involving square roots and constants
NEXT STEPS
  • Research the derivation of the formula T = 2π√(R/g)
  • Explore the concept of apparent weight in rotating systems
  • Investigate the effects of increased rotational speed on gravitational forces
  • Learn about the relationship between radius and rotational speed in circular motion
USEFUL FOR

Physics students, educators, and anyone interested in the dynamics of rotational motion and gravitational effects on objects in circular paths.

eunhye732
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The Earth rotates about its axis with a period of 24.0 h. Imagine that the rotational speed can be increased. If an object at the equator is to have zero apparent weight,
(a) what must the new period be?
(b) by what factor would the speed of the object be increased when the planet is rotating at the higher speed? Note that the apparent weight of the object becomes zero when the normal force exerted on it is zero.

For part (a), I know that T= 2(pie)sqrt(R/g)
I was wondering how you find R.
And I don't understand what (b) is asking for.

Thanks!
ps: if this question has already been asked, I'm sorry! :rolleyes:
 
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eunhye732 said:
I was wondering how you find R.

What circle does the object describe in 24 hrs ? What's its radius ?
(ok, correct, the data are NOT in the problem description ; they must be considered general culture :-)
 
well, my teacher told me that it's suposed to be a numberical answer. Thanks anyways
 

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