A motorcycle is driving along the walls of a round ring, which is rotating at [tex]\omega_0[/tex]. Its speed is constant V, in the same direction of the ring itself. Its mass is m, and the radius of the ring is R. I need to find the normal force that the walls exert on the motorcycle.(adsbygoogle = window.adsbygoogle || []).push({});

If we look at the problem from the motorcycle's reference frame, then it is stationary in a frame that is rotating at [tex]\omega[/tex] = ([tex]\omega_0[/tex] + V/R), so the normal force is equal to the centrifugal force:

[tex]N = m\omega^2R = m(\omega_0 + \frac{v}{R})^2R[/tex]

Now, if we look at this from the ring's reference frame, then the motorcycle is moving at a constant speed V inside the ring which is rotating at [tex]\omega_0[/tex]. Then we also need to take into account coriolis effect (right?), and the forces in the radial axis are:

[tex]N + 2m\omega_0v - m\omega_0^2R = 0[/tex]

But the normal force is the same, no matter which frame we use, so:

[tex]m\omega_0^2R - 2m\omega_0v = m(\omega_0 + \frac{v}{R})^2R[/tex]

[tex]\omega_0^2 - 2\omega_0\frac{v}{R} = (\omega_0 + \frac{v}{R})^2[/tex]

And that's obviously incorrect... so can someone please point out my mistakes?

Thanks,

Chen

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# Homework Help: Rotating systems

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