Lesson 2 of 10

Frame of Reference & Coordinate System

参考系与坐标系

Today's question

Sitting still on a speeding subway: are you moving or not?

Lesson notes

A short written version of Lesson 2. The study sheet has more practice questions.

Short answer

It depends on the reference frame. Relative to the train car, you are not moving. Relative to the ground, or an ad board outside, you are moving fast with the train.

Key ideas

Without a reference frame, you cannot say whether an object is moving or at rest.
A reference frame is an object or system chosen to study motion and assumed to be at rest.
A frame is not truly at rest. It can be chosen freely. In high school, the default frame is the ground.
With a different frame, the same object has a different state of motion.
To find the frame, find the verb and its subject. Whoever moves is not the frame; whoever does not move is.
A coordinate system is a frame with a ruler. A 1D position needs one number, 2D two, 3D three. Coordinates need units.

Step by step

First choose a reference frame. Without one, "moving or not" has no answer.
Frame 1: the train car. You sit still in the car, so relative to the car you are not moving.
Frame 2: the ground, or an ad board outside. The train races forward and carries you, so you are moving, and very fast.
Same person, two frames, two answers. Whether you move depends not on you, but on the frame you choose.
So name the frame: "At rest relative to the car, moving relative to the ground."

Common mistakes

Wrong: "I can just look and see if it moves." Right: moving always means moving relative to a frame. Choose the frame first.
Wrong: "A frame must be at rest relative to the ground." Right: a frame can be chosen freely. It can be moving or not.
Wrong: taking the moving object as the frame. Right: the frame is the one that does not move. In "the bridge flows", the frame is the water.
Wrong: ignoring the axis direction or the units. Right: if downward is positive, points above O are negative. Always write units, like −2 m.

Practice

Question 1. An ancient poet once wrote: "Empty-handed, I hold a hoe; on foot, I ride a water buffalo. I walk on the bridge: the bridge flows, the water doesn't." In "the bridge flows, the water doesn't," "the bridge flows" should be understood as choosing which object as the reference frame? ( )
A. Water
B. Bridge
C. Person
D. Ground

Show the answer

A. "Flows" has the bridge as its subject, so the bridge is moving. "Doesn't flow" has water as its subject, so the water is not moving. The one that is not moving is the frame: water.

Question 2. A ball falls from 5 m above the ground, bounces off the ground, and is caught 1 m above the ground. The origin is set 2 m directly below the release point, and downward is the positive direction of the axis. What are the position coordinates of the release point, the landing point, and the catch point, respectively? ( )
A. −2 m, 3 m, 2 m
B. −2 m, 2 m, 1 m
C. −2 m, −2 m, −1 m
D. 4 m, 0, 1 m

Show the answer

A. Downward is positive, so points above O are negative. Release point: 2 m above O, so −2 m. Landing point: 5 − 2 = 3 m below O, so 3 m. Catch point: 3 − 1 = 2 m below O, so 2 m.

Words in English and Chinese

reference frame, frame of reference: 参考系
coordinate system: 坐标系
origin: 原点
positive direction: 正方向
at rest: 静止
heliocentrism: 日心说
geocentrism: 地心说
one-dimensional (1D): 一维

Sum it up before you move on.

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What was the question?
What is the simple version?
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