Pendulum on Earth and another planet different periods radii

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SUMMARY

The discussion centers on calculating the period of a pendulum on Earth compared to another planet with a significantly smaller radius. The user initially miscalculated the period due to neglecting to square the radius in their formula. After correcting this error, they arrived at a period corresponding to a radius of 11,200 km. The conversation emphasizes the importance of following structured templates for calculations and deriving formulas symbolically for clarity.

PREREQUISITES
  • Understanding of pendulum motion and gravitational effects
  • Familiarity with the formula for the period of a pendulum
  • Basic algebra skills, including squaring numbers
  • Knowledge of how to derive formulas symbolically
NEXT STEPS
  • Study the formula for the period of a pendulum in detail
  • Learn how to derive gravitational equations for different celestial bodies
  • Explore the implications of radius on pendulum motion
  • Review guidelines for structured problem-solving in physics
USEFUL FOR

Students studying physics, educators teaching mechanics, and anyone interested in understanding pendulum dynamics across different planetary environments.

James Ray
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Member advised to type out equations and not to use images only of handwritten scratchwork

Homework Statement



Screenshot_2016-05-18-19-42-16.png

Homework Equations



The Attempt at a Solution



20160518_214314.jpg
 
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James Ray said:

Homework Statement



View attachment 100919

Homework Equations



The Attempt at a Solution



View attachment 100920
The radius seems very small (a factor of 10 less than Earth's radius. But I can't see any mistake in the solution.
 
Your result is wrong. You should use the template and type in your work.
 
ehild said:
Your result is wrong. You should use the template and type in your work.
I forgot to square the radius in the first calculation.
 
James Ray said:
I forgot to square the radius in the first calculation.
Now I get 11200 km.
 
It is all right now, but how did you get it? I see quite a lot of unnecessary calculations on your sheet of paper. It would be very easy if you derived the formula for R2 symbolically.
 

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