(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The linear momentumpof a particle of mass m is given by

p=(L/r)n

wherenis 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 vectorrwhich gives the direction of the position of the particle relative to O.

b)calculate the corresponding torque, and from this result find forceFon the particle.

c) Show that the magnitude of the force on the particle can written

F=(L^{2}/mb^{3})sin^{3}θcosθ

2. Relevant equations

3. The attempt at a solution

Here's what I did:

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

b)T= dL/dt

L d/dt[rXn] = L (dr/dt Xn+rX 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 knowF= dp/dt soF= (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?

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# Angular momentum, torque, & force on a particle

Can you offer guidance or do you also need help?

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