We use the classroom shown on the right to discuss reference frames. The classroom
shows a professor on a skateboard and Katherine, a student in the professor’s class.
The professor conducts a demonstration in the class: He throws an eraser up, and
catches it in the same hand. The professor does all this while moving across the
classroom on a skateboard. Both the professor and Katherine have stopwatches to
measure the time interval between “the throw” and “the catch”.
In Concept 1, we show what Katherine observes. She sees the professor moving by at
a speed v. The blue arc shows the path of the eraser from her reference frame. It
moves both vertically and horizontally in projectile motion. A grid is shown in the
illustration. Each side of the grid is 1.0 meter. Katherine sets the position of the “throw”
at(x = 0,y = 0) m, and the catch at (3.00, 0) m. The eraser reaches its peak at (1.50,
1.50) m in her reference frame.
Katherine can also establish the time coordinates of these events. She starts her
stopwatch when the professor throws the ball, so the throw is at t = 0 s. He catches the
ball at t = 1.11 seconds.
In Concept 2, we show the exact same series of events as observed in the professor’s
reference frame. He considers himself as stationary and views the class as moving by. It is the same experience as looking out the window of
an airplane: You consider yourself stationary as you sit in a seat, and the ground is passing by.
In his reference frame, the eraser travels solely vertically. Its initial and final positions are (0, 0) m. Its peak position is (0, 1.50) m. He also has
a stopwatch, which he also starts when he tosses the eraser. His observations of the time (to the precision of this stopwatch) are identical. He
throws the ball at t = 0.00 s, and catches it at t = 1.11 s. To describe the catch, he could describe its space time coordinates as (0 m, 0 m,
0 m, 1.11 s). The first three coordinates state its x,y and z position, and the last states the time.
The conclusion of all this: Reference frames determine the observations made by observers. Katherine observes the eraser moving
horizontally as well as vertically; the professor sees it move only vertically.
You may object: But does the professor not know he is moving? Should he not factor in his motion? Consider throwing an eraser up and down
and catching it. Did you catch it at (roughly) the same position? In your reference frame, perhaps your classroom, the answer is “yes”. But to an
observer watching from the Moon, the answer is no, since the Earth is moving relative to the Moon.
There is no correct inertial reference frame. Katherine cannot say her reference frame is better than the reference frame used by the professor.
Measurements of position, time and other values made by either observer are equally valid.
In your earlier studies, you were asked to assume that the time intervals in each reference frame were identical. At the speed the professor is
moving, and to the hundredth of the second, the two observers measure the same time interval. However, if the professor were moving at, say,
75% of the speed of light, the time intervals would be quite distinct. Discussing how measured time intervals change as the observers’ relative
speeds approach the speed of light is a major topic in this chapter.
Reference frame
Motion is perceived relative to a
reference frame35.2 - Events and observers
Event: Something that can be pinpointed using
position coordinates and time.
Observer: Person who records where and when
an event occurs in a particular reference frame.
The definition of an event may accord with your own sense of the word í it is something
that occurs at a specific place and time. A bat striking a ball is an event; the ball striking
the glove of a fan in the bleachers is another event. In physics, a “Saturday night dance”
isnot an event, since it does not occur at a specific time or a specific enough location.
In the illustrations to the right, we consider a single event: The professor on the train
kicks a soccer ball. He is standing on a train that is moving at a constant velocity on the
track. Another observer, Sara, stands on the ground and observes the same event, the
professor kicking the soccer ball. An observer is someone who records when and where
something occurs in a reference frame.
Both agree that the professor kicked the soccer ball, and that it rolls along the train. But they use different reference frames to describe where
and when the soccer ball was kicked.
In Concept 2, you see the position and time of the event described using Sara’s reference frame. She uses a set of position markers on the
ground. (You can see markers like this, though at a scale greater than meters, on railroad tracks and highways). In her reference frame, the
ball was kicked at the position 2.8 meters, and her watch tells her it was kicked at 5:00 PM Pacific Standard Time.
In Concept 3, we show the same event, but now the professor describes it using his reference frame. He measures position using a scale on
the train. Using that reference frame, he states that he kicked the ball at the position 0.7 meters. He also has not changed his watch since he
set out on his journey, so his watch tells him that he kicked the ball at 8:00 PM Eastern Standard Time.
These two sets of observations can be reconciled, but they illustrate how the reference frames of the two observers determine the coordinates
An event
“Something that happens at a specific
time and location”
Example: Professor’s foot meets ball