Radial component of a velocity vector - cylindrical coordinates

[Matty Mooo]

Hi there,

I'm trying to determine the radial component of a velocity vector in a disk. The vector doesn't (necessarily) start from the centre of the disk and can be pointed in any direction. I've attached a .pdf with the schematics - it seems like a simple problem but it has me stumped.

The magnitude and a direction are given (see the attachment).

If someone could direct me in the right direction that would be awesome. I am familiar with cylindrical coordinates, but I just don't know where to start with this one..

Matty.

PS; This isn't homework!

 

[HallsofIvy]

The "radial component" of a vector is the length of its projection onto the line y= x.

 

[Matty Mooo]

Hi,

Thanks for the reply. Although, I'm not sure you understand the problem.

Imagine looking down on top of a disk (with centre at R=0). Then imagine a body, somewhere on the disk (R $$\neq$$ 0). This body is then given a 'kick' with velocity v₀ in a direction determined by the "known angle" in the above attached file. In the frame of the centre of the disk, the body will have a $$\phi$$ velocity component and an R velocity component. Is it possible to find v_R, the radial component of the body's velocity, as measured in the frame of reference of the centre of the disk?

The above problem is working in cylindrical coordinates (R, $$\phi$$, h), where h, the thickness of the disk, is neglected.

Apologies if I'm not explaining myself properly!

Matty.

PS; There are some other variables I can provide. Also, even a small velocity approximation would suffice for now.