Non-inertial Frame of Reference 1
A non-inertial frame of reference is a coordinate system which is accelerating. That is, its velocity vector 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 an animation of a non-inertial frame of reference which would be experienced in an elevator ride, 'Pause' and 'Restart' buttons included.
The Elevator:
- Non-inertial frame when accelerating (changing velocity)
- Inertial frame when not accelerating (constant velocity)
[1] Zero velocity at bottom:
The elevator is standing still at the bottom of the shaft with a constant velocity of zero. The elevator is not accelerating.
Since its velocity is constant, the elevator at this moment is an inertial frame of reference. If you were in the elevator, you would feel your own weight as you would normally.
[2] Increasing velocity upward:
The elevator is moving upward and its speed is getting greater and greater. The elevator is accelerating.
Since its velocity is not constant, the elevator at this moment is a non-inertial frame of reference. If you were in the elevator, you would feel more than your normal weight. You could imagine a fictitious force on you pulling you down and making you feel heavier.
Actually, the floor of the elevator is pushing up on you in order to get you moving up along with the elevator.
[3] Constant velocity upward:
The elevator is moving upward and its speed is not changing. The elevator is not accelerating.
Since its velocity is constant, the elevator at this moment is a inertial frame of reference. If you were in the elevator, you would again feel your normal weight. You would feel no fictitious forces.
[4] Decreasing velocity upward:
The elevator is moving upward and its speed is getting less and less. The elevator is accelerating.
Since the velocity is not constant, the elevator at this moment is a non-inertial frame of reference. If you were in the elevator, you would feel less than your normal weight. You could imagine a fictitious force pulling you up on you making you feel lighter.
Actually, the floor of the elevator is slowing down and you are,
momentarily, continuing upward, moving a bit away from the floor. In a
small manner, as you fall back to the floor, you feel lighter much like
you would in free fall.
[5] Zero velocity top:
The elevator has stopped and has zero velocity at the top of the shaft. The elevator is not accelerating.
Since the velocity is constant, the elevator at this moment is a inertial frame of reference. If you were in the elevator, you would feel your normal weight just as you had at the bottom and middle of the ride where the velocity of the elevator was also constant.
[6] Increasing velocity downward:
The elevator is moving downward and its speed is getting greater and greater. The elevator is accelerating.
Since its velocity is not constant, the elevator at this moment is a non-inertial frame of reference. If you were in the elevator, you would feel less than your normal weight. You could imagine a fictitious force on you pulling you up and making you feel lighter.
Actually, the floor of the elevator is moving away from you, and you are falling down toward it.
[7] Constant velocity downward:
The elevator is moving downward and its speed is not changing. The elevator is not accelerating.
Since its velocity is constant, the elevator at this moment is a inertial frame of reference. If you were in the elevator, you would again feel your normal weight. You would feel no fictitious forces.
[8] Decreasing velocity downward:
The elevator is moving downward and its speed is getting less and less. The elevator is accelerating.
Since the velocity is not constant, the elevator at this moment is a non-inertial frame of reference. If you were in the elevator, you would feel more than your normal weight. You could imagine a fictitious force pushing you down and making you feel heavier.
Actually, the floor of the elevator is slowing down and you are
running into it.
[9] Zero velocity at bottom:
The elevator is standing still at the bottom of the shaft with a constant velocity of zero. The elevator is not accelerating.
Since its velocity is constant, the elevator at this moment is an inertial frame of reference. If you were in the elevator, you would feel your own weight as you would normally. This inertial frame of reference would be equivalent to the inertial frame experienced when the elevator was traveling at a constant velocity in the central portion of the upward or downward motion.
Above, the white rectangle represents an elevator. We can take physics measurements relative to it. Using its walls, ceiling, or floor as references to measure from, the elevator becomes our frame of reference.
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. Its acceleration is zero. So, it is an inertial frame of reference. There are no fictitious forces, the law of inertia holds.
[2] The elevator begins to move upward. 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 with the start of its motion and is now on its way up traveling at a constant velocity. It is not accelerating. Now, like in [1], it is an inertial frame. The extra weight felt during the prior acceleration is no longer present. The elevator, although moving, is now again an inertial frame with no fictitious forces. Your weight would feel normal.
[4] The elevator begins to slow to a stop. It is slowing down, and, therefore, its velocity is changing. It is again accelerating. So, it is now a non-inertial frame of reference. Fictitious forces are present. A person feels lighter, as if he or she were 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, part [1]. 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. You feel normal weight.
[6] The elevator begins to move down with its speed getting greater and greater. 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. It is not accelerating. This is an inertial frame of reference, and everything feels normal. There are no 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.
[9] The elevator is again at the bottom, standing still. It is an inertial frame since it has a constant velocity of zero. It is not accelerating. Note that this inertial frame is equivalent to the ones when the elevator was moving up or down with a constant velocity in parts [3] and [7]. That means physics experiments done when your frame of reference is still will show the same results as similar experiments done in a moving, constant velocity frame of reference.
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 direction changes, the velocity changes. Click the link below to jump to an explanation of a non-inertial frame caused by a change in direction. Fictitious forces arise under this condition also.