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Math Help - mechanics - polar coordinates

  1. #1
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    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!
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  2. #2
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    Re: mechanics - polar coordinates

     F(r)=\frac{m}{r^5}
    Since force is in the radial direction,we only have centripetal acceleration which would be \frac{1}{r^5}
    \Rightarrow \omega^2R=\frac{1}{R^5} \Rightarrow \omega=\frac{1}{R^3}
    \Rightarrow T=\frac{2\pi}{\omega} \Rightarrow T=2\pi R^3
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    Re: mechanics - polar coordinates

    Quote Originally Posted by ignite View Post
     F(r)=\frac{m}{r^5}
    Since force is in the radial direction,we only have centripetal acceleration which would be \frac{1}{r^5}
    \Rightarrow \omega^2R=\frac{1}{R^5} \Rightarrow \omega=\frac{1}{R^3}
    \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?
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  4. #4
    Junior Member ignite's Avatar
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    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 View Post
    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
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