Non-inertial Frame of Reference 1
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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.
The Elevator
Non-inertial Frame When Accelerating
Inertial Frame When Velocity Is Constant
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. Go back to the previous page and click on the other link to 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.
Note: The background for this repeating VRML animation turns blue at the start of its presentation. Apparently, due to timing problems associated with downloading VRML worlds over the Internet, you may have to wait several seconds before you see the blue background and correctly view the animation cycle from its beginning. The wait is never over sixty seconds and is usually much shorter.
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