Teaching Physics by Oversimplification

Why Physics Teachers Preach Fiction
Posted by Tom Hartsfield, April 9, 2014

Have you ever wondered why hurricanes spin in only one direction in each hemisphere? How about why you get thrown against the side of your seat if you careen around a corner in your car?

You’ve probably heard the answers: the Coriolis and centrifugal forces, respectively. Trivia, yes, but there is more here than mere academic facts.

Physicists will name these forces to explain events, but then call them “fictitious.” Why? Well, partly because we’re a mathematically pedantic lot. Mostly though, it’s because, at the root of things, these forces don’t exist as physical pushes. They’re actually gateways from the very complicated real world to the slightly less complicated world of Isaac Newton.

Newton’s laws govern sets of objects found in common “reference frames.” A reference frame is like the backdrop for a play, the setting for a novel, or the grid work of a graph plot. The gridiron yard lines of football are a reference frame to describe the position of the ball and the players. Latitude, longitude and altitude are a (spherical) reference frame for places on earth.

Mathematically, a reference frame means a set of 3D coordinates that can be used to describe all of the objects and forces under consideration. The most difficult aspect of a physics problem can be choosing these coordinates in the way that makes the problem simplest to solve.

Newton’s laws live and work in reference frames that are inertial. That is, the frames do not accelerate. A parked car is an inertial reference frame. Taking off, speeding up, and braking are non-inertial. Put the car on cruise control, and you are back in an inertial reference frame.

Acceleration is a change in velocity. Speeding up or braking in a straight line is a change in the magnitude of velocity (speed). However, turning is also a change in velocity: a change in its direction. An object going in circles is doing nothing more than constantly changing the direction of its velocity, while staying at the same speed. Yet, this is still considered acceleration and is, hence, non-inertial.

Here’s where the fictitious forces fit in. They allow you to fudge a non-inertial frame to look like an inertial frame. Then you can use Newton’s laws to understand what is happening, instead of resorting to much harder physics [called “non-inertial reference frames”].

Centrifugal and Coriolis forces are the fictitious forces for translating rotating frames to inertial ones. This comes in handy not just for cars and merry-go-rounds, but for everything we do. Living on a giant revolving orb makes all of our frames slightly non-inertial.

The centrifugal force explains why you get thrown against the car door in a sharp turn. That’s because you’re rotating with the vehicle in a non-inertial frame. To someone standing on an overpass watching you pass under, there is no centrifugal force at all; inertia simply carries you in the direction you’d have been going before the turn. The door pushes you away from your straight-line path.

Given that we live on the surface of an enormous spinning object, none of our reference frames are truly inertial; they are all rotating, just a little bit. Most of the time the difference is so small that you can neglect it. But for things travelling a long way, it matters.

Airplane flights, hurricanes, missiles, artillery shells and other large things moving long distances appear to experience the Coriolis force. As the object travels through the atmosphere in a straight line from the surface, we spin underneath it. From the ground, it looks like the plane is turning. The pilot sees his plane flying a straight line and the earth below falling away.

The Coriolis force also dictates the direction of cyclonic rotation in a hurricane. Air is attracted to the low-pressure center of the storm, but while the air travels in a straight line toward the center, the earth beneath rotates away. Missing and passing by the low-pressure center, the air is pulled back in again, forming a spiraling vortex.

Meteorologists must always account for the effects of the fictitious forces not only for hurricanes but all low-pressure systems. The rest of us only have to worry about them when playing racer on our commutes. Or when asked to solve a physics problem in college.

Tom Hartsfield is a physics PhD candidate at University of Texas.

http://www.realclearscience.com/blog/2014/04/why_physics_teachers_preach_fiction.html

Tom Hartsfield is a regular contributor to the RealClearScience Newton Blog. He translates abstruse topics in physics, astronomy and mathematics into plain English. He has taught university physics courses and currently performs in a physics circus for elementary school children. He is a Ph.D. candidate in physics at the University of Texas at Austin, where he is conducting research on optics and semiconductors. He also holds a bachelor's degree in physics from New College of Florida.