Physical pendulum made of a uniform disk

[aigerimzh]

Homework Statement

A physical pendulum is made of a uniform disk of mass M and radius R suspended from a rod of negligible mass. The distance from the pivot to the center of the disk is l. What value of l makes the period a minimum?

Homework Equations

The Attempt at a Solution

 

[Spinnor]

The period T = 2∏√(L/g) see equation (1),

http://en.wikipedia.org/wiki/Pendulum

If you want T small make L small. Or do I not understand your problem %^)

 

[gneill]

In this case the pendulum is an extended object, not a point mass on the end of a massless rod or string. When the rod or string has mass, or if the bob is not a point mass, you would consider the pendulum to be what's called a "physical pendulum".

In such cases you may want to look at the pendulum in terms of angular motion and moment of inertia. There is an expression for the period that involves the moment of inertia about the pivot point. You'll have to do a little research or calculus...

 

[Spinnor]

So would this be close?

 

[gneill]

So would this be close?

That's the right idea. Can you solve the differential equation and find an expression for the period?

 

[Spinnor]

That's the right idea. Can you solve the differential equation and find an expression for the period?

I might be able to and hopefully aigerimzh can as well %^)

 

[aigerimzh]

Thanx! Very Much)