mechanics - polar coordinates

A particle of mass m moves under the influence of a central force which attracts a particle with force of magnitude F(r) = m/(r^5). Assuming that the particle moves on a circular orbit of radius R where R = constant, find the period of particles motion.

Any help would be lovely, thanks!

Re: mechanics - polar coordinates

$\displaystyle F(r)=\frac{m}{r^5} $

Since force is in the radial direction,we only have centripetal acceleration which would be $\displaystyle \frac{1}{r^5}$

$\displaystyle \Rightarrow \omega^2R=\frac{1}{R^5} \Rightarrow \omega=\frac{1}{R^3} $

$\displaystyle \Rightarrow T=\frac{2\pi}{\omega} \Rightarrow T=2\pi R^3$

Re: mechanics - polar coordinates

Quote:

Originally Posted by

**ignite** $\displaystyle F(r)=\frac{m}{r^5} $

Since force is in the radial direction,we only have centripetal acceleration which would be $\displaystyle \frac{1}{r^5}$

$\displaystyle \Rightarrow \omega^2R=\frac{1}{R^5} \Rightarrow \omega=\frac{1}{R^3} $

$\displaystyle \Rightarrow T=\frac{2\pi}{\omega} \Rightarrow T=2\pi R^3$

thank you very much, also i have another question....I was given the differential equation (d^2u/dphi^2) + 4/9u = 0 and told to show that the particle will eventually move along the line phi = 3pi/4...any idea how to start?

Re: mechanics - polar coordinates

Please post entire question giving details like what is u and 'phi' and initial conditions.

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Re: mechanics - polar coordinates

Quote:

Originally Posted by

**ignite** Please post entire question giving details like what is u and 'phi' and initial conditions.

This is the one, I can do all of it aside from the last part