Understanding Centripetal Force: How It Works in an Inertial Frame

[kushan]

If the net sum of forces is zero , the object moves with constant velocity.(inertial frame)
But , when this centripetal thing comes in
Suppose we have only a force acting perpendicular to the motion of the body.
then how does this centripetal force comes in , there are 4 fundamental forces and all other forces can be taken from these forces , but centripetal force ?
which fundamental force makes centripetal force ?
and why is that when a satellite revolving around a planet , acted by gravity, force is equated to mv^2/r , but that is analogous to F=ma , so there is only one force acting that is gravity so satellite should fall but it doesn't ...
what is my thinking lacking ?

 

[rcgldr]

For a moving (non-zero velocity) object, you can separate any force vector into two vectors, a force in the direction of velocity (changes speed), and a force perpendicular to velocity (centripetal force - changes direction). Even if the force is always perpendicular to velocity, it can produce about just about any path (other than sharp corners). For example imagine the possible paths of a car moving on a flat plane at constant speed with only steering inputs.

 

[kushan]

which fundamental force causes centripetal force then?
and why does centripetal force acts radially inwards
if that happens then a satellite should go down as gravity is also acting inwards and centripetal also inwards?//.

 

[Doc Al]

then how does this centripetal force comes in , there are 4 fundamental forces and all other forces can be taken from these forces , but centripetal force ?
which fundamental force makes centripetal force ?

Centripetal force is just the name we give to a force acting towards the center of some circular motion. The particular forces that give rise to the centripetal force depend on the particular circumstances. In the case of a satellite in orbit around a planet, gravity provides the centripetal force.

and why is that when a satellite revolving around a planet , acted by gravity, force is equated to mv^2/r , but that is analogous to F=ma , so there is only one force acting that is gravity so satellite should fall but it doesn't ...

Since the satellite is centripetally accelerating, there must be a net centripetal force (provided by gravity). Since that force remains perpendicular to the motion, the satellite continually changes direction. Note that forces cause changes in velocity. Since the force acts towards the planet, the change in the satellite's velocity is towards the planet. (If the satellite were not moving, then it would surely fall. But it is moving--at just the right speed to maintain a circular orbit.)

 

[rcgldr]

In the case of a satellite in a circular orbit, speed² / r = acceleration from gravity at that distance (r) from the center of earth, so it follows a circular path. In this case the acceleration only changes the direction of velocity, without changing it's path or speed. The satellite is always accelerating towards the earth, but it's velocity perpendicular to that acceleration causes it to remain in a circular path.

If the orbit is elliptical, then most of the time gravity is not perpendicular to velocity, and speed will change, fastest when closest to earth, slowest when farthest away from earth. In a two body system, (earth and satellite as only two objects in the universe), the center of mass of the two body system doesn't accelerate.

Which fundamental source is centripetal doesn't matter. In the case of a satellite in a circular orbit, it's gravity, but the force could be magnetic (a moving charged object curves perpendicular to a magnetic field), or mechanical force like a test tube in a centrifuge.

 

[Doc Al]

which fundamental force causes centripetal force then?

In your example with the orbiting satellite, gravity provides the centripetal force.

and why does centripetal force acts radially inwards

Gravity acts toward the center of the planet.

if that happens then a satellite should go down as gravity is also acting inwards and centripetal also inwards?//.

Careful. Gravity is the centripetal force. Only one force acts: gravity. And the satellite accelerates, in accordance with Newton's 2nd law.

 

[pongo38]

kushan "what is my thinking lacking ?" You are thinking of a static situation. This is a dynamic case.

 

[kushan]

Thank you doc al and rcgldr , that helped a lot , can you give other instance in which other fundamental force causes centripetal force .
i want to know why is centripetal force acting radially inwards ?

 

[rcgldr]

Thank you doc al and rcgldr , that helped a lot , can you give other instance in which other fundamental force causes centripetal force.

I already listed gravity, magnetic, and mechanical as possible forces. You could also have an electrical (charge) causing centripetal force.

I want to know why is centripetal force acting radially inwards?

This is by definition. As mentioned, if centripetal force varies over time, the path isn't circular, it could be a spiral, ellipse, sine wave, ..., just about any path as I mentioned before with the car moving at constant speed with just steering inputs example.

Other than zero centripetal force and a straight line path, then at any point in a curved path there is a "radius of curvature", the equivalent of the radius a tiny bit of a circular arc that would correspond to the curvature of the path at that point. It's always inwards by definition, since the direction of the "radius of curvature" would be "inwards" of the curved path.

 

[Neandethal00]

If the net sum of forces is zero , the object moves with constant velocity.(inertial frame)
But , when this centripetal thing comes in
Suppose we have only a force acting perpendicular to the motion of the body.
then how does this centripetal force comes in , there are 4 fundamental forces and all other forces can be taken from these forces , but centripetal force ?
which fundamental force makes centripetal force ?
and why is that when a satellite revolving around a planet , acted by gravity, force is equated to mv^2/r , but that is analogous to F=ma , so there is only one force acting that is gravity so satellite should fall but it doesn't ...
what is my thinking lacking ?

Whatever way the physicists explain centripetal force, graphical or analytical, I still feel centripetal force is not totally understood.

It appears to me if the rotating object is tied by some physical means to the center of rotation, the force is towards the center, but if the object is not tied to the center then the force is away from the center. Water in a bucket spinning in a vertical circle, satellites are examples of latter case.

 

[Doc Al]

It appears to me if the rotating object is tied by some physical means to the center of rotation, the force is towards the center, but if the object is not tied to the center then the force is away from the center. Water in a bucket spinning in a vertical circle, satellites are examples of latter case.

No, in all cases the net force is toward the center. The bucket (and gravity) pushes the water toward the center; gravity pulls the satellite towards the center.

 

[Neandethal00]

No, in all cases the net force is toward the center. The bucket (and gravity) pushes the water toward the center; gravity pulls the satellite towards the center.

Say whatever you like, but the following equality is disturbing to me

mv²/r = GMm/r²

This equality may not be exact, but it does the job.

 

[azureth]

There is a centripetal acceleration for an object that is moving along a non-straight curved path so according to Newton second law there must be a centripetal force,which might be a component of the total force, acting on it .

 

[Doc Al]

Say whatever you like, but the following equality is disturbing to me

mv²/r = GMm/r²

This equality may not be exact, but it does the job.

Why do you find that disturbing? And why in the world do you think that it implies that for an orbiting satellite the force is outward?

That equation is just an expression of Newton's 2nd law applied to something in a circular orbit.

 

[kushan]

Hey neanderthal, yea it is little confusing for beginners like us
If you imagine two forces acting at centre , it gives you a picture of an object also moving towards centre .

 

[rcgldr]

mv²/r = GMm/r²

This just means that the actual centripetal force, GMm/r², equals the centripetal force required to produce a circular path, mv²/r. When they are equal, then it's just two different ways to describe the same centripetal force.

 

[kushan]

ok , when we change frame of reference how does centripetal force become centrifugal force and start to act outwards?

 

[Doc Al]

ok , when we change frame of reference how does centripetal force become centrifugal force and start to act outwards?

It doesn't. The centripetal force, being a 'real' force, exists in all frames. However, in order to apply Newton's laws in a rotating frame various 'fictitious' forces must be introduced. One of them is the outward centrifugal force. (See: Fictitious force)