Vector components in Polar Coordinate

[changazi]

Hi!

In a non-uniform circular motion if I have two components of a vector in cartesian coordinates then how to find the tangential and radial components of a vector. For example ;

I have Vx and Vy as horizontal and vertical components of a vector V respectively. Vx and Vy can lie in all for quadrants.

First I convert this into polar form as

|V|=sqrt(Vx^2 + Vy^2)

Tangent (angle)=(Vy/Vx)

From this conversion from cartesian to polar coordinates that I have found out now, how can I find the Tangential and radial components of the Vector V in polar coordinates or saying in other way that if I have two components of a vector in cartesian coordinates then from this information how can I find the two components of that vector in polar coordinates.

Immediate help is needed SOS!

 

[CompuChip]

Welcome to PF changazi.

I don't really think I understand your question, didn't you just write down the polar coordinates of V? The only thing you need to take care with is the angle (you can take the arctangent, but you might have to add/subtract something to make sure it lies in the right quadrant -- you can easily see how to do this if you draw a picture of the vector).

 

[thomate1]

Hi there!

In order to find the tangential and radial components of a vector in polar coordinates, you can use the following formulas:

Radial component = |V| * cos(angle)

Tangential component = |V| * sin(angle)

Using the information you have provided, you can plug in the values for |V| and angle (calculated using Vy and Vx) into these formulas to find the respective components in polar coordinates. It is important to note that the angle must be in radians for these formulas to work properly.

I hope this helps! Let me know if you have any further questions. Good luck with your calculations!