Golf Skeptic- at the risk of feeling like I'm wasting my time- and since Bucket O' Bucket has called me a mediator
- I'll jump in and participate by having you read the following excerpt that I found on the internet. It would help me if you could read this and tell me if you agree with it or have issues with it. Because since I understand what they are saying in the article I'll know more about your perspective if I understand if you are in agreement with the article or how you might differ with their article.
INTERNET ARTICLE
A non-inertial frame of reference does not have a constant velocity. It is accelerating. There are several ways to imagine this motion:
· The frame could be traveling in a straight line, but be speeding up or slowing down.
· The frame could be traveling along a curved path at a steady speed.
· The frame could be traveling along a curved path and also speeding up or slowing down.
Such an accelerating frame of reference is called a non-inertial frame because the law of inertia does not hold in it. That is, an object whose position is judged from this frame will seem to spontaneously change its velocity with no apparent non-zero net force acting upon it. This completely violates the law of inertia and Newton's laws of motion, since these laws claim that the only way an object can change its velocity is if an actual non-zero net force is applied to the object. Objects just do not start to move about here and there all on their own.
This is really quite easy to understand. If you are in an automobile when the brakes are abruptly applied, then you will feel pushed toward the front of the car. You may actually have to extend you arms to prevent yourself from going forward toward the dashboard. However, there is really no force pushing you forward. The car, since it is slowing down, is an accelerating, or non-inertial, frame of reference, and the law of inertia no longer holds if we use this non-inertial frame to judge your motion.
If all of this is viewed relative to the ground, it becomes clear that no force is pushing you forward when the brakes are applied. The ground is stationary and, therefore, is an inertial frame. Relative to the ground, when the brakes are applied, you continue with your forward motion, just like you should according to Newton's first law of motion. The situation is this: the car is stopping, you are not; so, you head out toward the dashboard. From your point of view in the car it seems like you have spontaneously been pushed forward. Actually, there is no force acting on you. The imagined force toward the front of the car is a fictitious force.
A similar fictitious force can be noticed by a person in a car when it speeds up. Let us say that you are in a car at a stop light. The car is standing still. The light turns green, and the car accelerates forward. While undergoing this acceleration, the car is a non-inertial frame of reference. If the acceleration is large enough, you will feel yourself "pushed" into the seat. Actually, no force is pushing on you. Again, as viewed from the inertial frame of the ground, you are just maintaining your velocity, as you should according to Newton's first law of motion. You were still when the light was red, and you are attempting to remain still when the light turns green. However, the car started to move when the light turned green. The car actually comes up from behind you, and, using the seat, the car pushes you forward. As the seat comes forward and pushes on you, the back seat cushion compresses a bit. You may interpret this feeling as your body being pushed backward into the seat. Really, you are attempting to maintain your velocity of zero, and the seat is coming up from behind to push on you. There is no backward force. The imagined force is a fictitious force. Fictitious forces arise in non-inertial, or accelerating, frames of reference.
There are several ways to describe a non-inertial frame. Here are a few descriptions:
· A non-inertial frame of reference is a frame of reference with a changing velocity. The velocity of a frame will change if the frame speeds up, or slows down, or travels in a curved path.
· A non-inertial frame of reference is an accelerating frame of reference.
· A non-inertial frame of reference is a frame of reference in which the law of inertia does not hold.
· A non-inertial frame of reference is a frame of reference in which Newton's laws of motion do not hold.
· In a non-inertial frame of reference fictitious forces arise.
What follows here are two demonstrations that show non-inertial frames of reference. The first one is an animation of a non-inertial frame which acts like an elevator. The other shows an animation of a rotating frame of reference. Rotating frames of reference are non-inertial frames since they are following curved paths. Remember that a change in direction, which would occur along a curved path, constitutes a change in velocity, and, therefore, constitutes an acceleration. If the frame accelerates, it is a non-inertial frame.
A non-inertial frame of reference is a coordinate system which is accelerating. That is, its vector velocity is not constant. So, it is either changing its speed by speeding up or slowing down, or it is changing its direction by traveling in a curved path, or it is both changing its speed and changing its direction.
Below is a VRML animation of a non-inertial frame of reference similar to that which would be experienced in an elevator ride. Please see this note if at first the animation does not seem correctly presented or synchronized.
Above, the yellow platform with the x, y, z coordinate axes represents an elevator. During certain portions of its travel an elevator constitutes a non-inertial frame of reference. As it goes up and down it speeds up or slows down over portions of its path. During these periods of changing speed the elevator is accelerating and, therefore, is a non-inertial frame of reference. Over other portions of its path the velocity of the elevator is constant. At these times it represents an inertial frame of reference.
When you watch the above animation, be aware that its motion should be considered in several parts. Those parts are:
1. The elevator is at the bottom and is not moving. Its velocity is constantly zero, and, therefore, its velocity is constant. So, it is an inertial frame of reference. There are no fictitious forces, the law of inertia holds.
2. The elevator begins to move up. It is speeding up, and, therefore, its velocity is changing; it is accelerating. So, it is a non-inertial frame of reference. There are fictitious forces present. One feels pushed into the floor a bit; one feels heavier. However, this is a fake force. Really, a person is just trying to stay at his or her prior velocity, which was zero. The floor is coming up from underneath and pushing on the person. The person feels pushed into the floor.
3. The elevator is done starting to move and is now on its way up, traveling at a constant velocity. Now it is an inertial frame. The extra weight felt during the acceleration is no longer present. The elevator is now an inertial frame with no fictitious forces.
4. The elevator begins to stop. It is slowing down, and, therefore, its velocity is changing; it is again accelerating. So, it is once again a non-inertial frame of reference. Fictitious forces are present. A person feel lighter, as if he or she was being pulled up a bit. Actually, the person is just trying to maintain his or her prior velocity. The person was going up and continues to go up. The floor, however, is stopping and is no longer traveling as fast as the person. So, the person feels lifted off of the floor.
5. The elevator is stopped at the top. This is just like being stopped at the bottom. And it is just like part 3. The velocity is constant, that is, constantly zero. The elevator is an inertial frame now, and there are no fictitious forces.
6. The elevator begins to move down. This is an acceleration, and the elevator is again a non-inertial frame of reference. A fictitious force arises. The person feels lighter, as if pulled up. But he or she is just trying to remain still, and the elevator floor is falling away.
7. The elevator is traveling at a constant velocity on the way down. This is an inertial frame of reference, and everything feels normal. There are not fake forces.
8. The elevator slows down while moving downward. Again, this acceleration creates a non-inertial frame. A person in the elevator would feel heavier, would feel pushed down. Actually, the person is just trying to maintain his or her downward velocity and the slowed down floor is getting in the way.
Such an elevator ride is an excellent example of a frame of reference that changes from an inertial frame of reference to a non-inertial frame of reference as the speed of the velocity changes from a constant value to a changing value respectively.
However, there are other non-inertial frames of reference which are caused by changes in velocity other than changes in speed. Remember that when an object changes direction, it changes its velocity. Since velocity is made up of speed and direction, when the speed changes, the velocity changes. Next we’ll cover an explanation of a non-inertial frame which is due to a change in direction, that is, a rotation. Fictitious forces arise under this condition also.
Near the edge of the disk is an x, y, z coordinate system which is, of course, following a curved path. This coordinate system is moving in circular motion. The speed of the coordinate system is constant; however, it is accelerating. It is accelerating because its velocity is changing. Its velocity is changing because the direction of its movement is changing, and, since velocity is made up of both speed and direction, when the direction changes, the velocity changes. So, this coordinate system is an example of a non-inertial frame of reference. Non-inertial frames are accelerating frames.
Since it is a non-inertial frame of reference, one should feel a fictitious force if one is in the frame. And one would; it would be especially noticeable if the disk were spinning quickly. One would feel pushed off of the disk. This force is often called the centrifugal force; it is a fictitious force. It really does not exist.
Actually, if you were near the edge of this disk, at any moment your velocity would be tangent to the circle in which you were moving. You would be like the blue dot which you could imagine moving in a circle as in the following diagram.
Now, pretend this spinning is happening with you on a children's merry-go-round; almost everyone has been on one of those. At the moment depicted above, you are the blue dot, and your velocity is tangent to the circle. According to Newton's first law, which is really just a restatement of the law of inertia, you should continue to travel in a straight line tangent to the circle. That is, you would try to maintain your velocity and move along the line tangent to the circle as shown in the next diagram.
However, you will want, we will suppose, to stay on the merry-go-round. To do that you will have to "hang on" by pulling yourself toward the center of the circle. Most likely you will grab on to the bars or posts mounted on the merry-go-round and pull yourself inward like the next diagram shows.
Very most likely, however, you will interpret the pull you provide toward the center as your attempt to fight being pushed away from the center of the circle. This force does not really exist, however. You would not be being pushed away from the center. You are just trying to go in a straight line and must provide a center seeking force to make you go around the turn and stay on the merry-go-round.
This fictitious force away from the center of rotation is called the centrifugal force. The force you apply, pulling yourself back in toward the center and keeping you on the merry-go-round is called the centripetal force.
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