- #1
Slvtmong00se
- 10
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In uniform circular motion, (eg, a mass on the end of a string moving in a horizontal circle) centripetal force is the only thing causing acceleration. we have the kinematic relationship V=RW
or velocity is proportional to radius. I.e a bigger radius means greater linear speed?
For the motion of a satellite in Earth orbit in uniform circular motion, we have centripetal force due to gravity alone. Equating the force of gravity to centripetal force we obtain
V=square root of :(GM/R)
i.e. speed is now INVERSELY proportional to orbital radius.
I don't understand what's going on here. How can a centrally directed force, being the only thing causing acceleration, lead to two different relationships between V and R?
or velocity is proportional to radius. I.e a bigger radius means greater linear speed?
For the motion of a satellite in Earth orbit in uniform circular motion, we have centripetal force due to gravity alone. Equating the force of gravity to centripetal force we obtain
V=square root of :(GM/R)
i.e. speed is now INVERSELY proportional to orbital radius.
I don't understand what's going on here. How can a centrally directed force, being the only thing causing acceleration, lead to two different relationships between V and R?