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

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The discussion revolves around solving a vector mechanics problem involving a block moving down a cylinder in polar coordinates. The user derived an equation for the maximum angle of contact using normal tangential coordinates, expressed as theta = cos^(-1)(2/3 + Vo^2/(3gX)). However, they seek guidance on how to approach the problem using polar coordinates, as their assignment requires solutions in both systems for full credit. There is some confusion about whether normal and tangential coordinates can be considered the same as polar coordinates in this context. The user is looking for clarification on how to represent the solution differently in polar coordinates while ensuring accuracy.
Bobafable
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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
 
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Welcome to PF!

Hi BOB! Welcome to PF! :smile:

(have a theta: θ and try using the X2 and X2 tags just above the Reply box :wink:)
Bobafable said:
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 :redface: …

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