# Angular momentum, torque, & force on a particle

1. Feb 28, 2009

### bcjochim07

1. The problem statement, all variables and given/known data
The linear momentum p of a particle of mass m is given by

p=(L/r)n

where n is a fixed unit vector, L is a constant, and r is the distance of the particle from a fixed point O.

a) calculate the angular momentum L of the particle relative to point O. Express the result in terms of L, n, and the unit vector r which gives the direction of the position of the particle relative to O.

b)calculate the corresponding torque, and from this result find force F on the particle.

c) Show that the magnitude of the force on the particle can written
F=(L2/mb3)sin3θcosθ

2. Relevant equations

3. The attempt at a solution

Here's what I did:

a) L = r(r X Ln/r] = L(r X n)

b) T = dL/dt
L d/dt[r X n] = L (dr/dt X n + r X dn/dt)

c) I'm not quite sure how to use the result in part b to obtain this answer, and I think this is part of my problem. But I do know F = dp/dt so F = (L/r) dn/dt

d) This is the part of the problem that I am most unsure about. Could somebody give me some suggestions or tell me if I did something wrong in the above steps?