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

[Chewy0087]

Homework Statement

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

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;

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!

 

[Chewy0087]

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

 

[tomcue]

I would suggest approaching the tricky pendulum question on page 6 by first reviewing the concepts of center of mass and moment of inertia. These concepts are important in understanding the motion of a pendulum. Next, I would recommend carefully reading the question and making sure to properly substitute the given values into the equations. It may also be helpful to draw a diagram to visualize the situation.

For the 24 hour question, it seems like you have made some progress by calculating the difference in time period and the difference in r. However, it is important to also consider the factors that affect the time period of a pendulum, such as the length, mass, and gravitational acceleration. Additionally, make sure to use the correct formula for a pendulum with a mass on the end.

Regarding question 6 on page 10, it sounds like the concept you are looking for is the inscribed angle theorem, which states that an inscribed angle in a circle is half the measure of the intercepted arc. This theorem can be used to solve the problem by setting up an equation using the angles and arc lengths given. It may also be helpful to draw a diagram to visualize the situation.

Overall, my advice would be to carefully review the concepts and equations involved in pendulum motion, and to take your time when solving these problems. Don't be afraid to ask for help or clarification if you are stuck on a particular question. Good luck!