Angular Momentum of Uniform Disk Question

[sailaka]

1.Provide the question and knowns
A uniform disk turns at 3.7rev/s around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk's diameter, is dropped onto the freely spinning disk. they then turn together around the spindle with their centers superposed. What is the angular frequency in rev/s of the combination.[/b]



2. Homework Equations
This is the question I have. I'm not really sure on how to start the problem or what equation to use. I am thinking it may have to do with w=2(pi)f, where w is the angular frequency and f is the frequency, but I'm not quite sure. Any help on how to start the actual problem would be greatly appreciated. Thanks.

The Attempt at a Solution

 

[Hootenanny]

Welcome to Physics Forums.

A good place to start would be to think about which quantity would be conserved in this case?

 

[sailaka]

Thanks for making me feel welcome hootenanny and thanks for helping me get started on this problem. So I've figured out that the quantity being conserved is the Angular Momentum, but would the falling block make a difference? Thanks again for the help.

 

[cepheid]

Two other good questions to ask yourself would be,

"Which quantities does angular momentum depend upon?"

and

"Has the addition of the block changed anyone of those quantities?"

If so, then the other quantities must change accordingly, if angular momentum is to be conserved.

 

[sailaka]

Thanks again for the help guys

so mass, velocity and radius are the quantities that are depended by angular and since the block has been added it would double both radius and mass correct?

So the equation to figure out this problem would be L=2r_x*2m*v?

and angular momentum is the same as angular frequency right?

 

[cepheid]

It would double the mass. I don't think that it would double the radius, not from the way I'm interpreting the problem. Based on the description, the block fits exactly onto the disk, NOT changing the extent of the overall rotating object.

Angular momentum and angular frequency are two very different things. Angular frequency is a measure of the rate of rotation...e.g. your engine is rotating at 1000 rpms (or whatever).

Angular momentum is measure of the momentum a system has due to its rotational motion.

 

[sailaka]

Ah I see now. Yeah the doubling of the radius was my error, sorry. But, one last question is how would the velocity be found?

 

[cepheid]

Umm...well if mass doubles and R stays the same, and L MUST remain the same (due to the conservation law), then what happens to v? In other words, what change must you make to v in order to keep L the same?

 

[borgwal]

The advice by cepheid is incorrect: you can't say that "R stays the same". What you have to use are the "moments of inertia" [look this up in your textbook!] of both the rod and the disc: they are not the same, even if they have the same mass and the same length/diameter.

Otherwise, yes, you use conservation of angular momentum with respect to the rotation axis.

 

[cepheid]

whoops. my bad.