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In a circle motion, where two objects have the same orbital times, but different radius, which one will have the biggest centripetal/centrifugal force? The outer or the inner one?

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closed as off-topic by Aaron Stevens, Thomas Fritsch, Jon Custer, stafusa, ZeroTheHero Sep 19 at 3:06

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  • 2
    $\begingroup$ Hint: $a = \omega^{2} r$ and $\omega = 2\pi/T$ $\endgroup$ – K_inverse Sep 17 at 7:13
  • $\begingroup$ Hint: both are rotate around the center of mass $\endgroup$ – Eli Sep 17 at 7:27
  • $\begingroup$ @K_inverse so it increases as the radius increases? $\endgroup$ – Melvin Sep 17 at 9:57
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$$ \frac{F_{c1}}{F_{c2}} = \frac{mr_1\omega_1^2}{mr_2\omega_2^2} $$ and $ \omega_1 = \omega_2 $, because $ \omega = \frac{2\pi}{T} $, and $T=const$ according task conditions, so $$ \frac{F_{c1}}{F_{c2}} = \frac{r_1}{r_2} $$ given that $ r_1 > r_2$, we get $$ \frac{F_{c1}}{F_{c2}} > 1 $$, thus increasing radius while keeping angular speed the same - increases centripetal force

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I am assuming:

  1. there is some force which act towards Centre for both of the masses,
  2. $F= m \omega^{2} r,$ $\omega=2\pi/T.$

Simple, clear: the more radius, greater the centripetal acceleration. Assume $w$ to be constant.

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