Illustration 9.2: Reference Frames

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In the two animations, we are given an example of a moving reference frame relative to Earth's (stationary) reference frame. The motion of the orange ball as seen in Earth's reference frame is depicted in the animation by the time, position, and velocity measurements, t, x1, and v1, respectively (position is given in meters and time is given in seconds). An observer is in another reference frame that is moving with a constant velocity with respect to the surface of Earth. The observer also takes down time, position, and velocity measurements as shown in the table and represented by t, x2, and v2 respectively. Animation 1 shows position and Animation 2 shows velocity. Restart.

How do we know that the observer in frame two is moving with respect to Earth's reference frame? At t = -2 s, the observer in Earth's frame sees the orange ball at -4 m and moving to the right at a constant velocity of 2 m/s. What does the observer on the other reference frame see? She sees the ball start at the same position, but the ball moves with a different velocity in her frame. She sees it move to the right with a velocity of 3 m/s. Therefore, relative to Earth, our observer in frame 2 is moving with a velocity of 1 m/s.

But in what direction does the observer move? Consider the following question first. What if the observer-in her frame of reference-saw the ball as stationary? We would conclude that the observer was traveling at the same velocity as the ball as seen from the reference frame of Earth. When we move in the direction of the motion of the ball, the ball's relative velocity decreases. Thus, when we move in a direction opposite to the motion of the ball, the ball's relative velocity increases. Therefore the observer is moving to the left, relative to the reference frame of Earth, at 1 m/s!

When a reference frame is moving uniformly (at a constant velocity) with respect to a nonaccelerating (inertial) reference frame, the moving frame of reference is also called an inertial reference frame.