My brother is having trouble solving this problem, its been awhile since I did this sort of problem and was wondering if anyone could help. Here's the problem:

A 1.5 kg ball and a 2.9 kg ball are connected by a 1.0 m long rigid, massless rod. The rod is rotating cw about its center of mass at 30 rpm. What torque will bring the balls to a halt in 5.0 s?

I think you need to find the moment of inertia and convert rpm into rad/s, but I can't remember it right.
Thanks!

__________________
-Randy Wakefield

1969 220D 4 speed (parts car)
1976 280C
1976 280S
1981 240D 4 speed (parts car)
1982 300D
1983 300TD (Ivory)
1983 300TD (gold)
1985 300TD (gray)
1987 190D 2.5
1970 280SEL (sold)
1977 240D 4 speed (sold)
1974 280 (rusted to death)
---
1927 Chevy 4 door sedan
1938 Chevy 2 door sedan
1950 Willys Jeepster
1955 Studebaker President 4 door
1977 Ford F250
1979 Glastron 17'
1948 John Deere A
1960 John Deere 2010
1979 Satoh S650G
--
2000 Bichon (Doby)

I think I've got this, but it's also been a while since I've done this type of calculation. Here goes:

I assumed 1 m was the center to center distance between the masses, and that the masses are rigidly coupled to the rod.

First, I found the center of mass for our uneven barbell:

I drew a free body diagram with the masses and rod, then assumed it to be stationary in a 1g envrionment due to being simply supported at the CG. I called the location of the 1.5 kg mass x=0, with the location of the 2.9 kg mass being x=1. Since it's a stationary rigid object, the sum of the moments about any point on the object will be zero. So I did a moment balance at x=0. At this point, we have a 2.9 kg*m (improper unit I know but it works here) torque in the clockwise direction balanced by an equal torque generated by the upward force of the simple support, which must be 4.4 (1.5+2.9) kg. So,

-2.9+4.4x=0

where x is the location of the CG. Solving the equality reveals x=.659.

Next I went back through some of my college books to find the formula for mass moment of inertia, which seems to be Im (I with an m subscript, just use your imagination)=mr^2.

I summed the moments of inertia of the two masses:

Im=(1.5x.659^2)+(2.9*.341^2)

which works out to .988 kg*m^2

Then I decided to apply conservation of energy so I found the kinetic energy of the uneven barbell

Ek=0.5*Im*w^2

where w (omega-use that imagination again) is 30 rpm or Pi rad/s to make the units come out right. This came to 4.88 joules (lots of things squared over lots of things squared comes out to joules-if I did this right).

Next I had to find a torque that if applied over five seconds would provide the same energy. Ek is also equal to the definate integral over time of the applied torque, which I assumed to be constant. I don't know how to type in the symbols and make it look pretty, but I came up with 5T=4.88, so the required torque should be 1.02 Nm.

Somebody care to check that?

__________________
Whoever said there's nothing more expensive than a cheap Mercedes never had a cheap Jaguar.

83 300D Turbo with manual conversion, early W126 vented front rotors and H4 headlights 401,xxx miles
08 Suzuki GSX-R600 M4 Slip-on 26,xxx miles
88 Jaguar XJS V12 94,xxx miles. Work in progress.
99 Mazda Miata 183,xxx miles.

Sorry, you lost me at "rigid, massless rod". If we're going to be making stuff up just to create the problem, why not allow us to just make stuff up to solve it. And if that's the case, here: Jesus can stop it.

This was my downfall in school. I aimed at the monkey.

MV

That is to simplify the problem

__________________
-Randy Wakefield

1969 220D 4 speed (parts car)
1976 280C
1976 280S
1981 240D 4 speed (parts car)
1982 300D
1983 300TD (Ivory)
1983 300TD (gold)
1985 300TD (gray)
1987 190D 2.5
1970 280SEL (sold)
1977 240D 4 speed (sold)
1974 280 (rusted to death)
---
1927 Chevy 4 door sedan
1938 Chevy 2 door sedan
1950 Willys Jeepster
1955 Studebaker President 4 door
1977 Ford F250
1979 Glastron 17'
1948 John Deere A
1960 John Deere 2010
1979 Satoh S650G
--
2000 Bichon (Doby)

I know. I'd love to have some perfectly rigid massless connecting rods for my cars. I'd like to get some of those frictionless bearings we had in physics class too. Between the two I'd probably pick up a good 5 mpg.

__________________
Whoever said there's nothing more expensive than a cheap Mercedes never had a cheap Jaguar.

83 300D Turbo with manual conversion, early W126 vented front rotors and H4 headlights 401,xxx miles
08 Suzuki GSX-R600 M4 Slip-on 26,xxx miles
88 Jaguar XJS V12 94,xxx miles. Work in progress.
99 Mazda Miata 183,xxx miles.

In college, we sometimes shared lists of engineer jokes. One of them was:

If you have ever assumed a "horse" to be a "sphere" because it makes the math easier, you might be an engineer

__________________
Whoever said there's nothing more expensive than a cheap Mercedes never had a cheap Jaguar.

83 300D Turbo with manual conversion, early W126 vented front rotors and H4 headlights 401,xxx miles
08 Suzuki GSX-R600 M4 Slip-on 26,xxx miles
88 Jaguar XJS V12 94,xxx miles. Work in progress.
99 Mazda Miata 183,xxx miles.