What is the solution to the tricky pendulum question on page 6?

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SUMMARY

The discussion focuses on solving a pendulum problem from the Oxford admissions test, specifically addressing the calculations for the center of mass (COM) of a uniform rod and a pendulum with a bob. The user substituted distances for the COM, using r/2 for the rod and r for the bob, and calculated the time period differences for materials like brass and invar, yielding results of 0.469K and 7.429K respectively. Additionally, the user seeks clarification on a geometric rule related to equilateral triangles inscribed in circles, indicating a need for further guidance on this concept.

PREREQUISITES
  • Understanding of pendulum physics and time period calculations
  • Familiarity with center of mass (COM) concepts in rigid body dynamics
  • Knowledge of geometric properties of equilateral triangles and circles
  • Basic proficiency in algebra and trigonometry for solving physics problems
NEXT STEPS
  • Research the formula for the time period of a simple pendulum and its dependencies on length and mass
  • Study the principles of center of mass for composite objects in physics
  • Explore the properties of equilateral triangles inscribed in circles and related geometric theorems
  • Investigate the effects of material properties on pendulum performance, focusing on brass and invar
USEFUL FOR

This discussion is beneficial for physics students, educators, and anyone preparing for physics admissions tests, particularly those focusing on pendulum mechanics and geometric principles.

Chewy0087
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Homework Statement

hey sorry about this again but I'm having trouble with some questions :o:

http://www.physics.ox.ac.uk/Admissions/undergraduate/admissions_test/tests07.pdf

The Attempt at a Solution



page 6) okay well the bit I'm not sure about here is that L(cm) seeing as it is the distance to the COM i substituted r/2 for the uniform rod and r for the one with the bob giving me;

forma.jpg


i guess it makes sense because it would go to my simplified versions when simplified

then with the 24 hour one it's really tricky...

i worked out how much a time period would be to give a difference of 1 day + 1 second, then I worked out what the difference in r would be which gave me;

0.469K for brass and
7.429K for invar, do you think that's reasonable?

note i used the formula for a pendulum of negligible mass and a mass on the end.and

page 10) question 6, I literally have no idea, i KNOW that it's a silly rule or something reguarding a equilateral triangle in a circle or some rule you can draw on however I'm just blank on this one, any pointers in the right direction would be great...

thanks again!
 
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bump, i know it's a lot to ask but some help would be great
 

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