Re: A question on Rotational Mechanics I can't understand

In article <1113082132.629377.260140@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
<Neruocomp@xxxxxxxxx> wrote:
>Hi I'm a physics student and I'm at my wits end. I have gone to the
>professor but I left thinking I did understand it. Well that was not
>the case and I don't want to go back and embarrass myself. So here is
>my question, which involves the Atwood machine. There are two masses,
>mass 1 is greater then mass 2, and are separated by a distance of 2h.
>What is their velocity when they pass each other. One way of doing this
>question is using the Work Energy Theorem, and that is the quick way
>and I got the right answer(Since doing the same thing with a sphere
>rolling down a slope, I get a very similar answer). But I want to know
>how to do it using rotational mechanics. I'm getting lost some where
>and I don't know what is going wrong. I posted a scan of my notes on my
>blog http://my-niche.blogspot.com/ for simplicity sake instead of
>trying to type it out here. Any help would be greatly appreciated.
>


If it's a freshman class I assume you have a massless and frictionless
string and pulley.

A weight is being pulled down by gravity, and pulled up by the other
weight.

ma = sum of forces

The acceleration would be constant, so the integral is easy.

I'm not sure where rotational mechanics comes in unless the pulley has a
significant moment of inertia. If that's the case, draw a diagram of the
apparatus so that you can identify the forces acting on each part.

Mass 1:
Assume it is on the left.
(1) The weight of mass 1 pulling down.
(2) The tension T1 of the string pulling up.

Mass 2:
Assume it is on the right.
(1) the weight of mass 2 pulling down.
(2) Thye tension T2 of the string pulling up.

Pulley:
Define clockwise rotation as positive.
(1) The tension T1 pulling counterclockwise.
(2) The tension T2 pulling clockwise.

That will give you three equations of motion. They're connected by a set
of constraints.

The string has a fixed length so the displacement, velocity, and
acceleration of mass 1 is the negative of the displacement, velocity, and
acceleration of mass 2.

The string has a fixed length, so for a pulley of radius r and angular
displacement theta,

r*theta = delta y2 = -delta y1

--
"Outside the camp you shall have a place set aside to be used as a
latrine. You shall keep a trowel in your equipment and with it, when you
go outside to ease nature, you shall first dig a hole and afterward cover
up your excrement." -- Deuteronomy 23:13-14
.

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