How Far Apart Are the Masses on the Dumbbell-Shaped Flywheel?

[Noctix]

Homework Statement

A 1.0- kg mass is attached to a string wrapped around a shaft of negligible mass and having a 6.0cm radius. A dumbbell-shaped "flywheel" made from two 0.500- kg masses is attached to one end of the shaft and perpendicular to its axis. The mass attached to the string is released from rest and allowed to fall 1m to the floor. It reaches a speed of 2.68 m/s just before striking the floor. How far apart are the masses of the dumbbell?

Homework Equations

(between dumbells) I=mr²

m₁=flywheel

m₂=weight

The Attempt at a Solution

KE(flywheel) + KE(weight)=PE(flywheel)+PE(weight)

the height of the flywheel is 0(right?), so i can take out PE(flywheel).

then I set up 1/2Iw² + 1/2m₂v² =m₂gh

i then change 1/2IW² to 1/2mr²v²/r² which then becomes 1/2m₁v²


i feel like something is really wrong here because my radius's cancel and those are what I'm solving for. also, i never used the given radius of the shaft, so i think I'm missing something there too. Do I have to include some kind of kinetic moment of inertia equation for the weightless shaft(i didn't think so because m=0...or maybe i just ignore m)? also, do i need the regular kinetic energy 1/2mv² of the dumbells along with their other kinetic energy 1/2Iw²??

Thank you a thousand times in advance for the help, it's greatly appreciated.

 

[Noctix]

I drew a picture of the problem. Please help, I really need it. :(

[PLAIN]http://img219.imageshack.us/img219/2420/physicsm.jpg

 

[tiny-tim]

Hi Noctix!

(btw, edit your first post rather than reply to it … members are far more likely to answer threads with zero replies! )

the height of the flywheel is 0(right?), so i can take out PE(flywheel).

That's right … PE only involves the centre of mass, and that stays in the same place!

i feel like something is really wrong here because my radius's cancel and those are what I'm solving for. also, i never used the given radius of the shaft, so i think I'm missing something there too.

hmm … careless notation …

use r for the radius of the cylinder, and R for the radius of the flywheel, and everything should be ok!

Do I have to include some kind of kinetic https://www.physicsforums.com/library.php?do=view_item&itemid=31" equation for the weightless shaft(i didn't think so because m=0...or maybe i just ignore m)?

No, when exam questions tell you that something is "weightless" or "light", that means you can ignore it.

also, do i need the regular https://www.physicsforums.com/library.php?do=view_item&itemid=132" 1/2mv² of the dumbells along with their other kinetic energy 1/2Iw²??

No, they're the same thing.

The KE of a rotating body is the rotational KE about the centre of mass, plus the KE of the centre of mass (which is zero in this case, since the centre of mass isn't moving).

(or it's the rotational KE about the centre of rotation)