# A particle that feels an angular force only

1. Oct 2, 2012

### retro10x

1. The problem statement, all variables and given/known data

"Consider a particle that feels an angular force only, of the form F=2mvw(theta direction). Show that r=Ae^theta + Be^-theta, where A and B are constants of integration."
v=dr/dt
w=d(theta)/dt

2. Relevant equations

F(theta)= 2mvw = m(r*(dw/dt)+2vw)

3. The attempt at a solution

So I can solve the F(theta) equation to find that r*(dw/dt)=0, hence dw/dt=0
and I can also solve the F(radial) equation to find that dv/dt=r*w^2
I also know that this question involves a separation of variables and then integrating
However the problem is that I don't know substitutions I can make to put the equations I have into a form that makes that possible. Any hints or ideas are appreciated ^-^

2. Oct 2, 2012

### voko

dw/dt = 0 means w = W = const. So the first equation is then dv/dt = Cr, where C = W^2 = const. Are you saying you don't know how to solve this equation?

3. Oct 2, 2012

### retro10x

Oh, thanks for pointing that out
dv/dt can written as v(dv/dr)
So 0.5v^2=0.5c*r^2+D ;where D is the constant of integration
v=sqrt(cr^2 +2D)=dr/dt
I end up with: t+E=intg[dr/sqrt(cr^2 +2D)] ;where E is the constant of integration
Wolfram Alpha can't even solve this integral :O
What am I missing?

4. Oct 2, 2012

### voko

That integral can be converted to $$\int \frac {adx} {\sqrt {x^2 + 1}}$$.