Period of Small Oscillations for Rigid Body Pendulum

[willisverynic]

Homework Statement

A pendulum consists of a light rigid rod of length 250mm, with two identical uniform solid spheres of radius 50mm attached one on either side of its lower end. Find the period of small oscillations (a) perpendicular to the line of centers, and (b) along it.

Homework Equations

Period = 2*pi*sqrt(I/MgR)
Parallel axis theorem: I = Icm + Md^2

The Attempt at a Solution

I tried simply applying the parallel axis theorem to a ball using Icm = 2/5mr^2 and d = sqrt(.25^2+.05+2) but this yields and incorrect answer. I believe this method would be wrong because it would give the same answer for both parts, which is not the case

Thanks

ps not sure if this belongs in advanced or not

 

[tiny-tim]

welcome to pf!

hi willisverynic! welcome to pf!

(try using the X² icon just above the Reply box )

I tried simply applying the parallel axis theorem to a ball using Icm = 2/5mr^2 and d = sqrt(.25^2+.05+2) but this yields and incorrect answer. I believe this method would be wrong because it would give the same answer for both parts, which is not the case

i suspect you're measuring from the pivot point rather from than the axis

the axis of rotation is through the pivot point, either North or East …

the parallel axis is through the centre of one sphere, and the distance between the two axes does depend on which way round they are