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Curl

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I want to find a function describing the motion of the particle undergoing the type of motion depicted.

Basically it is a particle on a rotating vane (constant angular speed) and at some time it is released. The particle will move along the edge to the tip of the vane (and eventually fall off). This is rotation on a horizontal plane, so gravity is pointing down into the page (or monitor screen).

[PLAIN]http://img203.imageshack.us/img203/5241/rotation.gif

Unfortunately, as you all know, I'm not good at math, so I got stuck. I tried this:

*Put a coordinate system on the ball. One direction is the r direction (along the vane) and the second is the theta direction (normal to r).

*I said the acceleration in the r direction is r*w^2, and in the theta direction is dr/dt*w

Anything I do from here becomes a mess.

Can anyone get a function for the motion of this particle? I know it must look like a snail shell type curve. Thanks.

Basically it is a particle on a rotating vane (constant angular speed) and at some time it is released. The particle will move along the edge to the tip of the vane (and eventually fall off). This is rotation on a horizontal plane, so gravity is pointing down into the page (or monitor screen).

[PLAIN]http://img203.imageshack.us/img203/5241/rotation.gif

Unfortunately, as you all know, I'm not good at math, so I got stuck. I tried this:

*Put a coordinate system on the ball. One direction is the r direction (along the vane) and the second is the theta direction (normal to r).

*I said the acceleration in the r direction is r*w^2, and in the theta direction is dr/dt*w

Anything I do from here becomes a mess.

Can anyone get a function for the motion of this particle? I know it must look like a snail shell type curve. Thanks.

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