I understand that acceleration is a change in velocity. I also understand that an object that is traveling with centrifugal motion can be keeping the same speed but would still be considered accelerating since it’s direction is changing. But what I don’t understand is why centrifugal acceleration is defined in that manner, and what happens if the object is deaccelerating as it travels? Does it reach a point where it ever has 0 acceleration while it is moving?
Wow, this is really basic dynamics. You might want to check out a high-school-level physics text at your local library, to fill in the stuff I’m likely to leave out in this post.
Velocity is a vector quantity, so it includes both a value (which you know as the scalar quantity, speed) and a direction. So, any quantity that measures change in velocity will be non-zero whenever either the speed or direction or both are changing. Therefore, an object moving in a circle will be accelerated, since it’s direction is changing, which implies that velocity is changing.
Acceleration is one of the key quantities in the basic equation of dynamics: F=ma. Any force applied to a mass will cause some sort of change in velocity: an acceleration.
Lastly, it is quite possible for an object to be moving with zero acceleration. Just imagine something moving in a straight line with a constant speed. The velocity isn’t changing, so there is no acceleration. This ignores friction, of course.
I realize I barely touched the high points here, but I think this would be a good point to stop. Any questions?
Thanks for posting Saltire, and I do have several questions. I understood how you could have 0 accelerating when moving in a straight line but what about if you have centrifugal acceleration? Also, why does a change in direction have to mean a positive acceleration? If you are traveling in a circle you would switch between traveling in the positive direction and the negative direction equally.
Acceleration is a vector quantity the same way that velocity is, so maybe it’ll be clearer if we talk about the direction of the acceleration.
When the motion is circular, the acceleration vector points toward the center of the circle. Why is that? Because that’s the direction you need to apply the force that causes the object’s path to curve.
Visualize a weight on the end of a string, being spun around in a circle. If it weren’t for the string, the weight would fly of in a straight line. Because the string exerts a force toward the center of the circle, the velocity vector of the weight is forced to constantly change, dragging the weight into a circular path.
As far as switching back and forth between the positive and negative directions, that is true for both the velocity and the acceleration at different points in the path. The point is it’s constantly changing.
Okay, I’ll try to add information to this discussion, but I’d like to second Saltire’s suggestion of going to the library for a good high-school level physics book. References found on the web can be aimed at a multitude of levels, and confusing if seen in a scattershot approach, but a well-organized book aimed at your current knowledge level can be a great aid in learning.
That said, let me first correct some nomenclature. There is centripetal acceleration, and there is centrifugal force, but while they are related, they are not the same thing. Centripetal acceleration is the acceleration of an object orbiting around a central point at a constant angular velocity. Centrifugal force, on the other hand, is a pseudoforce felt by objects in the orbit, from their frame of reference.
Second, acceleration can be positive or negative. Use of the word deceleration can be ambiguous, and is generally avoided when talking about physics, and the term negative acceleration is preferred. Thus, the acceleration of an object on Earth at sea level is approximately -9.8 m/s[sup]2[/sup].
As for the original post, centripetal acceleration is defined the way it is because Newtonian relativity says that the laws of physics are the same in all non-accelerating frames of reference. Transforming the equation into the frame of reference of the orbiting object, as it is accelerating, requires a lot of extra math that is not needed if you do the calculations in an inertial reference frame.
The answer to your question about the object decelerating depends upon precisely what situation you’re talking about. Do you mean that the force on the object gets less and less, or do you mean there is a force in the direction opposite of where the orbiting object is moving at any one time?
Finally, for your question about 0 acceleration, you can use the equation Saltire to get the answer you want, F = ma. That is, force equals mass time acceleration. To be more precise, F is the sum of all forces on the object. Dividing by m, then, we get F/m = a. Thus, acceleration is 0 only when all forces on an object sum to 0.
How I interpret this question is: suppose you’re slowing down at the same time that you’re going in a circle. Can the two accelaration cancel? The answer is no. Centripetal acceleration is always perpendicular to the direction of travel, while change of speed is always parallell to direction of travel. Therefore, these two accelearations are perpendicular, and can not sum to zero.
Acceleration is a vector. It is neither positive nor negative.