# When is the centripetal force the biggest? [closed]

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?

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

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• Hint: $a = \omega^{2} r$ and $\omega = 2\pi/T$ – K_inverse Sep 17 at 7:13
• Hint: both are rotate around the center of mass – Eli Sep 17 at 7:27
• @K_inverse so it increases as the radius increases? – Melvin Sep 17 at 9:57

$$\frac{F_{c1}}{F_{c2}} = \frac{mr_1\omega_1^2}{mr_2\omega_2^2}$$ 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
2. $$F= m \omega^{2} r,$$ $$\omega=2\pi/T.$$
Simple, clear: the more radius, greater the centripetal acceleration. Assume $$w$$ to be constant.