# Circular Acceleration

1. Jan 12, 2005

### gunnar

Is it correct to say that an object in circular motion has an outward acceleration. Does an electron stay in orbit around the nucleus because of an outward acceleration?

2. Jan 12, 2005

### dextercioby

First question: an object in circular motion has a centripetal acceleration due to the fact that its velocity vector,though not necessarily changing its modulus,changes its direction.This accleration points toward the center of rotation.However,in the own reference frame,he experiences an inertial force (hence acceleration) called "centriugal force" which has an outward direction.
Second question:An electron stays in "orbit",because QM says so...

Daniel.

3. Jan 12, 2005

### vincentchan

If you have no idea what QM is, the reason an electron stay in orbit is the same as the earth orbit around the sun... just replace gravity by columb force (positive charge attract negative charge.)

4. Jan 12, 2005

### dextercioby

Don't take it literally.A famous Nobel Prize winner (for chemistry,though he was a physicist :tongue2: ) took it litearally 94 years ago and he ended up being wrong...Deadly wrong...

Daniel.

5. Jan 12, 2005

### gunnar

In physics your told that there is an inward acceleration but in chemistry there is an outward acceleration that is balanced by the attractive forces between the electron and the nucleus. What is what.
PS. Who is this man that was wrong?

6. Jan 12, 2005

### vincentchan

the electron it self is accelerate INWARD, but its FEELS an OUTWARD FORCE (centriugal force)....same thing when your car is accelerating FORWARD, you feels a force pushing you BACKWARD.... the force YOU FELL is opposite to the motion...

7. Jan 12, 2005

### dextercioby

Are u sure??I mean are sure you're given those explanations??On normal basis,they should not differ.Vincentchan has given u a pretty good explanation.

Sir Ernest Rutherford.Planetary atomic model,1911.

Daniel.

8. Jan 13, 2005

### gunnar

My physics book tells me there is no such thing as a CENTRIFUGAL FORCE
the reason you feel a push backwards in an accelerated car is because you are in a different inertial frame than the car is in.

What I'm trying to understand is wether these statements in physics and chemistry are stated as a theory rather than a fact. It makes more sense to say there is an outward acceleration which would explain why the electron stays in orbit around the nucleus. Is it not true that Newtons laws are not fully aplicable in microscopic physics

9. Jan 13, 2005

### dextercioby

WRONG.The centrifugal force exists.

Nope,in the car,u're in a noniertial reference frame.That's why u're acted on by inertial forces.

In the second sentence,u used 2 negations.Are u saying that:"It is true that Newton's laws are fully applicable in microscopic physics".

Daniel.

10. Jan 13, 2005

### clive

Hi,

The equilibrium of circular motion can be explained in two important chapters of mechanics:
1. dynamics (inertial frames) and
2. statics (non-inertial frames).

An inertial frame is a frame in uniform motion (acceleration=0) whereas a non-inertial frame is accelerated (non-zero acceleration). It is obvious than a frame related to Sun is inertial whereas a frame related to Earth is not, because its circular (that is accelerated) motion!

I'll begin with a well known physical system: Earth+Sun.

1. DYNAMICS (Newtonian mechanics)
All Newton's laws work in inertial reference frames. In inertial frames are not allowed "inertial forces". This concept contradict the basis of newtonian mechanics. The second law in Newtonian mechanics is

F=m*a

If we are to write this law for Earth, we have

F_se=M_e*a_cp (1)

where F_se is the force between Sun and Earth (and is a centripete force because it maintains the circular motion), M_e the Earth mass and a_cp the centripete acceleration of Earth (pointing to the center of the trajectory (that is to the Sun in our example)).

2. STATICS
Now we are in a reference frame related to Earth (non-inertial obvious). In this frame Earth is at rest (no acceleration!!!!). The only real force is the interaction with Sun. If we apply directly the second law we get

F_se=0

and that can not be true!!!!!!!!
Then..........we suppose to have a force with the same direction and opposite sense in order to explain the obvious equilibrium of Earth and we denote this fictitious force as "inertial force". This force has the norm m*v^2/R and is pointing outward the trajectory. Now we write

F_se=F_cf (2)

Eq. (1) and (2) are two solutions for the same problem but in DIFFERENT REFERENCE FRAMES!!!!

WHEN WE DEAL WITH NEWTONIAN MECHANICS THE INERTIAL FORCES ARE NOT ALLOWED!!!!

Last edited: Jan 13, 2005
11. Jan 13, 2005

### Romperstomper

I think what your book is trying to say is that centrifugal force is a pseudo force, which is a force created by a non-inertial frame. The car example is an example of a pseudo force, but centrifugal force is caused by moving in a circular motion, so if the car was doing donuts, the force that pushes you to the side of the car is centrifugal force.

12. Jan 13, 2005

### clive

When we deal with an atomic system (H for example) we have:

1) In an inertial frame (related to the atomic nucleus). Dynamic problem.
=======================================================
The nucleus attracts the electron with a force F=e^2/4/pi/eps_0/r^2. This force is the centripetal force of the motion. In the inertial frame related to the nucleus, the electron has an acceleration (it changes continuous its velocity direction) -> the centripetal acceleration. The second law

F=m*a_cp.

F and a_cp have the same direction and sense (to the nucleus)!

2) In an non-inertial frame (related to the electron). Static problem.
===================================================
The nucleus attracts the electron with a force F=e^2/4/pi/eps_0/r^2. The acceleration is ZERO because the electron is at rest in its own frame. But because the system is non-inertial, we must account for the centrifugal force F_cf, with the norm m*v^2/R and opposite sense relative to the frame acceleration. The equilibrium condition is now

F=F_cf

But the problem with the equilibrium in atomic systems is not the mechanics but electrodynamics: any accelerated electrical charge emits radiation (energy). Then the energy of the system is decreasing with each new rotation and the electron will finally fall upon the nucleus. That is the reason physicists say classical physics fails when applied to atomic systems.

Last edited: Jan 13, 2005
13. Jan 17, 2005

### gunnar

thanks guys, it makes more sense to me now.

14. Jan 17, 2005

### Staff: Mentor

Very late, but:
While I agree that its wrong to say it doesn't exist, its not quite what it seems to be and thats why it gets the characterization:

When your car turns left, you feel an invisible force pushing you to the right. In acuality, the action force is your car door or seatbelt pushing you to the left: the force you feel pushing you to the right is the reaction force due to your inertia.