Understanding Centripetal Force: How It Works in an Inertial Frame

In summary, when an object is moving with constant velocity in an inertial frame, the net sum of forces acting on it is zero. However, when a centripetal force is present, it causes the object to move in a circular path. This force can be caused by any fundamental force, such as gravity, magnetism, or electrical charge. In the case of a satellite orbiting a planet, gravity provides the centripetal force, allowing the satellite to maintain a circular orbit. The centripetal force is always directed towards the center of the circular path, and can be calculated using the equation mv^2/r.
  • #1
kushan
256
0
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 ?
 
Physics news on Phys.org
  • #2
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.
 
Last edited:
  • #3
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?//.
 
  • #4
kushan said:
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.)
 
  • #5
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.
 
  • #6
kushan said:
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.
 
  • #7
kushan "what is my thinking lacking ?" You are thinking of a static situation. This is a dynamic case.
 
  • #8
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 ?
 
  • #9
kushan said:
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.

kushan said:
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.
 
  • #10
kushan said:
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.
 
  • #11
Neandethal00 said:
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.
 
  • #12
Doc Al said:
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.
 
  • #13
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 .
 
  • #14
Neandethal00 said:
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.
 
  • #15
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 .
 
  • #16
Neandethal00 said:
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.
 
Last edited:
  • #17
ok , when we change frame of reference how does centripetal force become centrifugal force and start to act outwards?
 
  • #18
kushan said:
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)
 

What is centripetal force?

Centripetal force is the force that acts on an object moving in a circular path, directing it towards the center of the circle. It is necessary for an object to maintain its circular motion.

How does centripetal force work?

In order for an object to move in a circular path, it must constantly change its direction. This change in direction is caused by a force acting on the object, which is the centripetal force. This force acts perpendicular to the object's velocity and towards the center of the circle.

What is the relationship between centripetal force and velocity?

The greater the velocity of an object moving in a circular path, the greater the centripetal force required to keep it in that path. This is because as the velocity increases, the object's tendency to move in a straight line also increases, requiring a stronger force to change its direction towards the center of the circle.

How is centripetal force calculated?

The magnitude of the centripetal force can be calculated using the formula Fc = mv²/r, where m is the mass of the object, v is its velocity, and r is the radius of the circular path. This force is measured in Newtons (N).

What is the difference between centripetal force and centrifugal force?

Centripetal force is the force that acts towards the center of the circle, while centrifugal force is the force that appears to act outwards from the center of the circle. Centrifugal force is simply a perceived force and does not actually exist, it is a result of the object's inertia wanting to continue moving in a straight line.

Similar threads

Replies
21
Views
1K
Replies
15
Views
2K
Replies
16
Views
1K
Replies
24
Views
1K
Replies
7
Views
1K
Replies
15
Views
818
Replies
6
Views
2K
Replies
5
Views
4K
  • Introductory Physics Homework Help
Replies
10
Views
524
Back
Top