Centripetal force in circular motion

Question

We know that when a body moves in a circle,the acceleration which is responsible for changing the velocity of the body is centripetal acceleration which acts toward the center and the force which is responsible is thus the centripetal force. But then we say that centripetal force is the net force(resultant of all forces) acting towards the center. I don't understand how this net force definition is derived rigorously from the main definition(which is force responsible for change of velocity). I mean what would have happened if there were more forces acring towards the center?Here is a particular example:

The earth is moving around the sun. Gravitational force is acting between them. Then we say $F_C=F_G$. But why is it so?What will happen if both $F_C$ and $F_G$ exist separately?Thanks in advance.

Answer 1

If a particle moves in a circular trajectory with uniform speed, this means the acceleration of the particle is in radial direction (towards the centre) (can be proved through calculus). As the acceleration is towards the centre always so it is called the centripetal acceleration.
Now, Newton's second law states that $\vec a=\frac{\vec F_{net}}{m}$. This means the acceleration of a particle determines the net force acting on the particle or the net force determines the acceleration of the particle.
Now acceleration is towards the centre, this means the net force acting on the particle is also towards the centre (and is called as centripetal force).
If it has some other component (tangential component), then it contradicts our observation that particle undergoes uniform circular motion.

Hope this helps!

Answer 2

Centripetal force is a name give to any force that acts towards the center in circular motion. It can either be an individual force, or the resultant of several forces. Its has a special name because such a force only changes the velocity direction, but not the speed.

It is not clear what you mean by having both $F_G$ and $F_C$ separately, what physical mechanism would be providing a separate $F_C$ in the earth sun system? $F_G$ points towards the center, so it is a centripetal force.

Answer 3

Centripetal force is the force which balances and cancel out the centrifugal force acting one a revolving body and helps it to stay in orbit. That's the case of earth and sun, here the gravitational force only acts between them thus the Centripetal force is the attractive force between them.[Note centrifugal force has same magnitude as centripetal force but opposite direction thus they cancel each other]. Now if you place two charged bodies(of opposite charges)one at the centre and another revolving it ,then Centrifugal force acting outward(of the revolving body) equals the centripetal force but an extra electrostatic attractive force acts between them which causes the revolving body and the fixed body at the centre to come towards each other. Here centripetal force is not the total force acting inward(towards centre) Here it is=> Centripetal Force+Electrostatic force Centripetal and centrifugal cancels eachother other and electrostatic force causes the bodies to approach eachother i.e extra inward force(Electrostatic force)acts on the revolving body.