# Time for Revolution (Rotating about the Center of Mass)

## Homework Statement

Two men with masses 70 kg and 120 kg rotate at 1 rpm on a frictionless surface and are attached by a 15 m rope.
If they pull the rope so that only 10 m is between them when they rotate, how long does it take to make 1 revolution?

## Homework Equations

Angular Momentum and Inertia

## The Attempt at a Solution

So I found the center of masses for when the distances are 15 m apart and 10 m apart. I assume that angular momentum is conserved since there's nothing that really seems to affect it when I read it.
So L = L
Then Inertia = sum mr^2
Hence (m1r1^2 + m2r2^2)w1 = (m1r3^2 + m2r4^2)w2 where r1, r2, are distances from the center of mass for the 15 m, and r3 and r4 are the distances from the center of mass for the 10 m distance.
I1w1 = I2w2; I'm kind of confused by most of the radian conversions and such.
For what I got I1 = 9947.4kgm^2 and I2 = 4420.8kgm^2
Putting this together I got 9947(2pi rad/60s) = 4421(w2) then w2 = 2 .3rad/s. I assume I did something wrong, also I can't figure how I would convert it to 1 revolution, would I divide it by 2pi*r?
I did try it however it should be 40 seconds given as the answer in my book which I did not get

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## Answers and Replies

Bystander
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9947(2pi rad/60s) = 4421(w2) then w2 = 2 .3rad/s
Check your arithmetic.
1 revolution, would I divide it by 2pi*r?
2π radians is one full circle. Multiplying by r gives you the length of the arc, or circumference.

Check your arithmetic.

2π radians is one full circle. Multiplying by r gives you the length of the arc, or circumference.
Okay thanks I'll look into it.
Edit: yeah I actually meant 2pir/w instead. Mistyped

Bystander
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I meant 2rpi/w. However that doesn't yield anything
It yields m/s, which you are not interested in for this problem. Pay attention to units.
What do you mean by checking my arithmetic?
When I suggest that you check your arithmetic, it means you've made an error, and you should go through your work and find it.

haruspex
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It is always better, for a raft of reasons, to work entirely symbolically, only plugging in numbers as the final step.
In this case, it would have avoided the conversion to rad/s and back, which seems to have confused you. You could have worked with rpm throughout instead, but keeping it symbolic you don't care about units until the numbers are plugged in.
By the way, the book answer is wrong, as I expect you will discover.