How Do You Solve a Vector Mechanics Problem in Polar Coordinates?

[Bobafable]

I have a block/particle that has an initial velocity of Vom/s horizontally and its starting at the top and it is moving down the side of a cylinder with a radius of X. Assume no friction. What is the maximum angle at which the block/particle will remain in contact with the cylinder?


So I derived it in normal tangential coordinates and got that

theta = cos ^(-1) ( 2/3 +Vo^2/(3gX))

Which I am confident is correct. But I also need to figure out how to do it in polar coordinates. So if anyone knows how to do it or knows where to start I would be greatful for any type of help!
Thanks
BOB

 

[tiny-tim]

Welcome to PF!

Hi BOB! Welcome to PF!

(have a theta: θ and try using the X² and X₂ tags just above the Reply box )

So I derived it in normal tangential coordinates and got that

theta = cos ^(-1) ( 2/3 +Vo^2/(3gX))

Which I am confident is correct. But I also need to figure out how to do it in polar coordinates.

I don't understand …

it's a cylinder, so normal and tangential coordinates are polar coordinates, aren't they?

 

[Bobafable]

Yes, I believe they are but my teacher asked me specifically to do them in both coordinates and the problem is broken up into 50% of the points are distributed to each coordinate system.
I have to get each coordinate system correct to get any points at all. So I kinda need to be sure that it is right. If they are the same, then how would I basically do the same work but represent it differently or sufficiently explain that they are the same. Or is there a way that I can do it polar that's different than my previous way.