Question

What is the centripetal force, exactly? In gravitation's case, is it the strength the gravity of the (say) Sun that would be needed to keep the Earth at that orbital distance at its speed?

Answer 1

Centripetal force is the force which is required to keep the body in circular motion..
If there is no centripetal force, object can no longer stay in circular motion.. In this diagram (where i intend to draw a stone tied at the end of rope, moving in a circular path), the centripetal force is provided by the tension in the rope. once the rope is cut, there is no tension, i.e. no centripetal force. so, the stone leaves the circular path. So, centripetal force is the one which is required to keep the body moving in circular track!

Mathematically centrifugal force is given by:\[F=\frac{mv^2}{r}\]where m is mass of object
v is velocity (linear velocity)
r is radius of circular path.

Answer 2

So, in a sense, it is not actually a force in itself, but a 'strength of force' that other 'pulling towards the centre' forces (i.e. gravity) have to meet in order to to keep it in orbit?

Answer 3

Basically, the problem I've got is:\[mv^2/r>mMG/r\]
Where the 'requirement of force strength to keep it in orbit' is larger than the force. this means that the satellite will fall inwards. Is this correct?

Answer 4

Do you mean \[\frac{mv^2}{r}>\frac{GMm}{r^2}\]

Answer 5

Yes.

Answer 6

Here, \[\frac{mv^2}{r}\]is centrifugal force, and\[\frac{GMm}{r^2}\]is centripetal force (provided by gravity)..
The thing is that when centrifugal force exceeds centripetal force, the object leaves circular track. They should both be balanced and equal..

Answer 7

If\[\frac{mv^2}{r}>\frac{GMm}{r^2}\]the satellite will not fall inwards. It will fly away..

Answer 8

Thanks, I undestand it now: my logic was the wrong way round before.

Answer 9

@ujjwal "The thing is that when centrifugal force exceeds centripetal force, the object leaves circular track."......i find this statement confusing. how can centrifugal F ever exceed centripetal F? centrifugal force is not even a real force.

Answer 10

also, when an object in circular motion, leaves its circular path, it flies out tangentially...not radially. so it cannot fly out because of centrifugal force, coz its direction is 'radially' outward.

Answer 11

Centrifugal force can exceed centripetal force.. For a satellite moving in a radius r, centripetal force is fixed and is equal to \[\frac{GMm}{r^2}\]And now , the centrifugal force is \[\frac{mv^2}{r}\]So, by increasing velocity, you can increase centrifugal force and it can exceed centripetal force which is fixed in this case.

In case of a stone tied to a rope (supposing the rope is unbreakable), the centrifugal and centripetal force will always be equal.. Increasing the velocity will increase centrifugal force but then the tension in the rope will also increase and increase centripetal force as well.. So, centrifugal and centripetal force will be equal.
Basically in this case, centripetal force is variable.... not constant as that in case of a satellite.

Answer 12

And yeah, the satellite will fly away tangentially if centrifugal force exceeds centripetal force...That will always be outwards and never inwards towards earth..

Answer 13

when centripetal force = gravitational force
mv^2/r = GMm/r^2
v^2 = GM/r
in this case, velocity IS constant.

Answer 14

so centrifugal force cannot exceed centripetal F.

Answer 15

you can increase the velocity.. Its an artificial satellite, not natural one.. you can increase the power.. boost it up!! and boom.. there is goes.... It will leave the path!

Answer 16

right...i got the part where it leaves the orbit. but it doesn't do so because of centrifugal F right?...we can see it as a case of 'absence of centripetal F'....or just 'weaker centripetal F'.

Answer 17

It is relative.. Centripetal is less or centrifugal is more.. both have the same meaning..
At least in physics such things have same meaning..

P.S. In physics, I go to school and school comes to me have the same meaning... :D

Answer 18

hm...got it. thanks!
just got one more question : centripetal force is necessary for uniform circular motion...or just circular motion?

Answer 19

For uniform and non-uniform circular motions, the acceleration is what matters, if there is tangential acceleration in addition to radial acceleration, circular motion would be non-uniform. If there is only radial acceleration, circular motion will be uniform.

Answer 20

yes, i know that. though, my question was different. anyway, i got the answer, so no worries!