Calculating Center Movement on Spinning Turntable: Cockroach on DJ Turntable

[pringle]

Homework Statement

Basically there is a cockroach on a turntable (DJ Cockroach). The turntable is spinning with angular velocity $\omege$. In addition to that, there is a vertical uniform velocity $v_{drift}$. Need to show that the center is moved by $\delta = \frac{v_{drift}}{\omega}$.

Homework Equations

None given but there isn't all that many equations of motion anyway.

The Attempt at a Solution

I mean, I tried doing this in cartestsion but it just won't work out.

 

[Simon Bridge]

Here - let me help...

1... Basically there is a cockroach on a turntable (DJ Cockroach). The turntable is spinning with angular velocity $\omega$. In addition to that, there is a vertical uniform velocity $v_{drift}$. Need to show that the center is moved by $$\delta = \frac{v_{drift}}{\omega}$$

2... None given but there isn't all that many equations of motion anyway.

... just because there are none given does not mean there are none at all. This section is to help you think through what is required.

3...I mean, I tried doing this in cartesion but it just won't work out.

... all right, I won't insist you show us that effort here... I can imagine.
So what other coordinate systems do you know about and what sort of overall symmetry does the problem have?

Apart from that, I don't think there is enough information in the problem statement. Can you copy out the problem statement you are given word-for-word?
i.e. what is the cockroach doing on the turntable? Is the turntable oriented horizontally and slowly being lifted at $v_{drift}$?

 

[pringle]

Bro I am sitting in a Plasma Physics class. I can do mechanics just fine. This problem is just mad. How do you relate the polar coordinates to cartesian coordinates

 

[pringle]

I mean via relative transformation

 

[gneill]

Pringle, if you can't provide a complete, unambiguous question with all required details then we are not in a position to help. We need to be able to understand the problem before we can know how to advise. Otherwise we'd just be guessing and hoping that advice given is relevant. Why take that chance?

In your opening post you state: "Need to show that the center is moved by $\delta = \frac{v_{drift}}{\omega}$."

Can you at least clarify what that means? Moves why? When? Over some unspecified time period? Over some particular angular rotation of the platter?

 

[Simon Bridge]

Bro I am sitting in a Plasma Physics class. I can do mechanics just fine. This problem is just mad. How do you relate the polar coordinates to cartesian coordinates

Polar coordinates are usually for 2D systems. Is your problem only 2D?

There are 3D versions of polar coordinates though - the transformations are available online.
I suspect you will benifit from the cylindrical-polar version, but I don't really know because your problem statement is incomplete. It there some reason for not including all the information?

 

[Simon Bridge]

@pringle: How did you get on?