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.