[Physics] Basics of centripetal force

centripetal-forcenewtonian-mechanicsrotational-dynamics

Suppose an object is moving in a circular path. We know that the net force that is working on that object is the centripetal force towards the center. But the object should have gone closer towards the center in that case due to the radially inward force working on it, but it doesn't. Why does the object remain on the circular path instead of going closer towards the center?

For people who would be introducing centrifugal force in this case, i have a doubt on this too. Centrifugal is a pseudo force that only works when we are in the frame of the rotating object meaning we experience a pseudo force that pushes us radially outward. When we are in this frame, does centripetal and centrifugal both work on us?

But let us stay in ground frame as of now. Then what is the cause of the object not being pushed radially inward due to the effect of centripetal force? I am asking this question to clear out my doubts for strengthening my basic concept of physics. Hope the physics lovers will find this question relevant.

Best Answer

The object does fall towards the centre. It just misses...

  • Imagine placing a satellite high up there and letting go. It will fall straight down and crash.
  • Now push it slightly sideways while letting go so it has a small sideways speed to start with. I still falls down, but it also falls a bit sideways. It crashes on the ground slightly to the side from before.
  • Now give an even greater sideways speed. It still crashes, but this time far to the side from the point that is directly underneath.
  • And now give an even greater start speed, so large that the satellite flies so much sideways that it misses Earth. It still falls, but it falls besides Earth. And doesn't crash into Earth.

After missing Earth, the satellite flies away from Earth on the other side. Soon gravity will pull it back again. And the same thing will happen all over - it will miss Earth again. This continues forever; this is an elliptic orbit. With an even greater sideways start speed, the elliptic orbit becomes wider until it at some specific sideways speed exactly becomes as wide as it is tall - now it is a circular orbit.

The sideways speed needed for achieving an exactly circular orbit is found via the centripetal-acceleration formula:

$$a_c=\frac{v^2}{r}.$$

In this case the centripetal acceleration will be the gravitational acceleration at the orbit.

This was an explanation of why objects in circular motion don't fall inwards towards the centre. The answer is that they do fall. They fall constantly. They just miss the centre constantly as well. No need for centrifugal effects to explain this. You are correct that the so-called centrifugal force is a fictitious force that does not exist in the inertial frame - it is merely a force "invented" to explain the "swung outwards" tendency that we feel from our own perspective (from the rotational frame) when sitting in a turning car, in a spinning carousel etc.

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