- #1

PhysicsKush

- 29

- 4

## Homework Statement

The picture illustrates a simple pendulum and and two physical pendulums ,all having the same length ,L. Class their period in ascending order.

## Homework Equations

T = 2π / ( I/mgh)

I = I

_{cm}+ mh

^{2}

I

_{cm}=(ML

^{2}/12)

## The Attempt at a Solution

I have found the period for first two objects :

T

_{1}= 2π√(L/g)

T

_{2}= 2π√(2L/3g)

The problem for me appears at the third system because h is defined as the distance between the center of mass of the rod and the pivot point. In the third situation, it seems to me that the pivot is at the center of mass , hence h=0 , but that would result in a division by 0 error.

I have tried cutting the rod in half so that L =L/2 and h = L/4 but after some algebra i end up with T

_{3}= 2π√(L/3g) , which is smaller than T

_{1}

The solution to the problem is T

_{3}> T

_{1}> T

_{2}

Any help would be apreciated.