# Relative motion

Relative motion refers to the motion of one object with respect to another. The thing that we are comparing to is called the frame of reference. For example, I am currently at rest with respect to my house, but I am moving very quickly with respect to the Sun.

It is impossible to say what the absolute motion of an object is; we can only talk about relative motion. If I am walking down a street, for example, I could make either of the following statements with certainty:

• I am moving at 10 m/s [E] with respect to the stationary car.
• I am stationary and the car is moving at 10 m/s [W] with respect to me.

Both statements are correct; in fact, they are equivalent. In the first, the frame of reference is the other car’s position. In the second, the frame of reference is my own position.

The confusion comes when we introduce a frame of reference independent of the two things being compared. Normally, if I say that I am moving towards a stationary car, it is assumed that the frame of reference is the Earth. In this case, I am actually asserting two things: that I am moving with respect to the Earth, and that the car is at rest with respect to the Earth. If I were to instead say that I am stationary and the car is moving towards me (which also contains two assertions), this would be a different claim. They cannot both be true.

Pretend you are on train A at night looking out the window, and you see train B moving west. The only thing you can be sure about is that B is moving west with respect to A (meaning A is moving east with respect to B). There are several possibilities for motion with respect to the Earth:

• A is at rest; B is moving west.
• A is moving east; B is at rest.
• A is moving east; B is moving west.
• A is moving east; B is moving east slower.
• A is moving west; B is moving west faster.

Unless you can see something that is known to be stationary with respect to the Earth, like a tree, you cannot possibly know which of the above statements is true. If the other train appears to not be moving (both are stationary with respect to each other), you are still ignorant of motion with respect to the Earth. Either both trains are at rest, or they are are moving with the same velocity.

A frame of reference in which objects obey the law of inertia (velocity does not change unless acted on by an unbalanced force) is called an intertial frame of reference. Suppose you are a passenger in a car making a tight left turn. It feels as if you are being thrown against the door. We attribute this to the a fictitious force called the “centrifugal force.” This is not a real force because you aren’t actually being pushed against the door—you are moving in a straight line with respect to the Earth while the car turns under you. Since your velocity with respect to the car changes without any force acting on you, the accelerating car is not an inertial frame of reference.