## Moment of Inertia

rrr
Posts: 5
Joined: Mon Jan 22, 2007 11:28 am

### Moment of Inertia

Could someone please helpt with #25:
Seven pennies are arranged in a hexagonal, planar pattern so as to touch each neighbor. Each penny is a uniform disk of mass "m" and radius "r". What is themoment of inertia of the system of seven pennies about an axis that passes through the center of the cental penny and is normal to the plane of the pennies?
The answer is (55/2) mr^2

I can see how to get that answer if the distance from the outer pennies to the axis of rotation is 3r. But why is it 3r and not 2r?

The link to the test is http://www.ets.org/Media/Tests/GRE/pdf/Physics.pdf

CPT
Posts: 77
Joined: Mon Jan 15, 2007 2:05 am
Just use the Parallel axis theorem, so you have moment of inertia of each penny is (1/2)mR^2, contribution from the six outer pennies is: (1/2)mR^2 + m(2R)^2 = (9/2)mR^2 each, totalling to (54/2)mR^2 in all. The central penny contributes (1/2)mR^2, so the total is: (55/2)mR^2.

Hope that's clear enough 