# Relative kinematics and radius of curvature

1. Nov 17, 2008

### springo

1. The problem statement, all variables and given/known data
(Only need help for b) I think but I'll post the whole problem)
(All values are SI units)
(O; i, j, k) orthonormal basis.
A particle moves following this law: r = 8t2 j
A disk with radius 2 in the plane XOY rotates around Z with constant angular speed: ω = 3 k.
At the time the particle is 2m away from the origin, find:
a) Velocity and acceleration for the particle with respect to an observer placed at the edge of the disk, linked to it.
b) Radius of curvature for the trajectory of the particle with respect to the observer.

2. Relevant equations
I got rid of a) I think:
For O being the observer and P the particle I found that:
OP = 2 [ cos(3t) i + (4t2 - sin(3t)) j ]
v = 24t2 i + 16t j
a = 96t i + (16 - 72t2) j
t = 1/2 therefore:
v = 6 i + 8 j
a = 48 i - 2j

3. The attempt at a solution
For b) I think I should use:
1/ρ = cos3(3t)*d2y/dx2
But how do I find d2y/dx2?
Or if this is not how it's done please correct me.

Thanks a lot for your help.

PS: The problem is originally written in Spanish so please bear with me if I mistranslated any word.

Last edited: Nov 17, 2008
2. Nov 18, 2008

### springo

Bump. Could someone give me hand? Thanks a lot.