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?
$\begingroup$
$\endgroup$
3
-
2$\begingroup$ Hint: $a = \omega^{2} r$ and $\omega = 2\pi/T$ $\endgroup$– K_inverseSep 17, 2019 at 7:13
-
$\begingroup$ Hint: both are rotate around the center of mass $\endgroup$– EliSep 17, 2019 at 7:27
-
$\begingroup$ @K_inverse so it increases as the radius increases? $\endgroup$– MelvinSep 17, 2019 at 9:57
Add a comment
|
2 Answers
$\begingroup$
$\endgroup$
0
I am assuming:
- there is some force which act towards Centre for both of the masses,
- $F= m \omega^{2} r,$ $\omega=2\pi/T.$
Simple, clear: the more radius, greater the centripetal acceleration. Assume $w$ to be constant.
$\begingroup$
$\endgroup$
$$ \frac{F_{c1}}{F_{c2}} = \frac{mr_1\omega_1^2}{mr_2\omega_2^2} $$ 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
answered Sep 17, 2019 at 9:59