Speeding Bikes and Cars Moving Backwards: The Importance of Reference Frames

Six or Nine Meme

I’m sure that, if you’ve spent enough time on the internet, you’ve seen the above meme at some point. Is that a six on the ground or a nine? The two people can’t seem to decide. However, neither can we, nor really can anyone, barring perhaps the person who wrote the symbol on the ground in the first place. This essentially means that they’re both right; the number is a six, but it’s also simultaneously a nine. It depends on how you look at it, or your point of view.

That’s basically what a reference frame is in physics. Reference frames are just various points of view. In each one, the qualities of different objects may be different, but they’re still physically consistent, and so no one reference frame is special. For example, if someone is standing five feet from a radio, while another is standing ten feet away, the two people will hear the radio playing at different volumes, but these volumes will still be physically consistent.

An important thing for reference frames is that they’re “stationary”, that is to say, an observer in that reference frame would not be themselves moving, but objects around them would be. This is actually why, for many years, people believed that the sun moved around the Earth. We share the same reference frame as the Earth, thanks to the law of inertia, and so from our reference frame, it appears like the sun moves around us.

But if reference frames are always stationary, and objects around them are moving, and no one reference frame is more special than any other, then that means how we measure velocity depends entirely on the reference frame. For example, let’s say you’re in a car, and someone standing still on the side of the road sees you going at 60 kilometers per hour (km/h). You pass by another car going 40 km/h, according to the person on the side of the road, and in the other direction, you see someone on a bike going at 10 km/h, according to the person on the side of the road.

In your reference frame, which has to be stationary, the other objects need to be moving proportionally. Specifically, the velocities of the objects in your frame are equal to the difference between the velocities in another frame. So, for example, in your frame, the person on the side of the road seems to be moving at 60 km/h “backwards”, or opposite your travel direction. The car seems to be moving at 20 km/h, again, in the direction opposite your travel direction, and finally, the biker seems to be moving at 75 km/h.

There are two main types of reference frames: the one above is called an inertial reference frame, and the other type is a non-inertial reference frame. The difference between the two is that the former is moving at a constant velocity, that is to say, it doesn’t accelerate in a reference frame. So, in my above example, your car isn’t accelerating, so it’s an inertial frame.

A non-intertial reference frame is, as the name suggests, a frame that accelerates. The reasoning for these names is that the inertial reference frames follow Newton’s third law, the law of inertia, while something in the acceleration causes non-inertial reference frames not to follow the law of inertia.

Reference frames are incredibly important in physics. They tell us a lot about the properties of different objects, and more importantly, sparked Einstein to come up with his famous theory of relativity. However, that deserves its own article, or a series of its own. Until then, stay safe, and keep learning.