Frames of Reference

    What you see depends on where you are. It's more than philosophy, it's science. We call this the frame of reference.

    The frame of reference is related to the whole "assumption of firm ground" mentioned on the main page. We assume that our point of view is somehow special, because it's ours. But sometimes this can get us into trouble.

    Here's the simplest way to look at frame of reference. Look to your right. What's there? Now turn around. Things that were on your right before are now on your left. You've changed your way of referring to locations...right became left, and in front of became behind. So far, nothing too weird, at least.
    Now try standing on your head, or otherwise turning upside down. Drop something, and you'll see it appears to fall upward. Sure, you know you're upside down, so it's not too confusing, but what if you watch things through an upside down camera? Or one that's been tilted on one side, so things fall from left to right?
    One more simple case. Think about sitting in your car, with a drink in the cupholder as you drive down the street at 20 miles per hour (or 32 kilometers per hour, if you prefer). To you, the drink is not moving, it's stationary in your frame of reference. But to someone on the street, the drink's moving at 20 miles per hour! Other than adding a speed onto everything, though, things still make sense to both you and the guy on the street. If you drop something inside the car, both you and the guy on the street see it accelerate downward at the same rate.

    All of the examples above share one thing in common...while labels may change, everything seems to work more or less normally. Sure, somethign may fall in the wrong direction, but once you realize that direction is "down" it all makes sense. These are called inertial frames of reference, where the only difference between someone in the frame and someone outside of the frame is either a simple shift of directions or the addition of a constant velocity.

    But what about cases where the frame of reference is speeding up, slowing down, turning or spinning? If you're in your car and speed up, your drink will slosh backwards in the container as if there was some mysterious force pushing it back (and you'll feel like something's pushing you back into your seat). If you turn right, the drink will slosh to the left. Your frame of reference, the car, is accelerating. We call this a non-inertial frame.
    In any non-inertial frame, you're going to see weird things happen. If you drop something while speeding up, it won't fall straight down, it'll fall down and back. But someone outside in an inertial frame (that was at rest with respect to you at the moment you dropped the ball) will see it fall straight down. To you, though, there's some additional force acting on the object and making it move backwards. While there's various techincal terms for this, I'm going to call all of these strange new forces frame effects. Effects of having your frame of reference accelerating somehow.

    Thus, whenever you try to figure out how things will move in an accelerating frame, you need to add up both the real forces (like gravity or friction or tension) and the frame effects. If you're accelerating in a straight line at a, then you get something like this:

Fyou see = Freal - ma

    The reason for the minus sign is that if your frame is accelerating forward, everything in it will seem to be forced backwards. Notice that in this simple case, all that matters is the acceleration of your frame, nothing else. When you're in a spinning frame, however, it gets trickier.

    Say you're in a rotating frame of reference, like a merry-go-round. It spins with an angular velocity of ω, in units of radians per second (there's 2π radians in a full circle). This is a vector, but don't worry about the details if you're not already familiar with them. So, if an object of mass m is moving at a velocity of vr with respect to the merry-go-round, at a position r away from the center, a bunch of math leads to the following:

Fyou see = Freal - mω×(ω×r) - 2mω×vr

    Ugly, isn't it? That first term after Freal, which only depends on where you are and how fast the frame spins, is called the centrifugal force, and it's always outward. It's the way things feel like they're being hurled outward when you go in a circle, when to an outside person they just look to be going in a straight line (or trying to). The second term, which depends on how fast you go? That is the Coriolis force.

    Keeping the two terms separate can get tricky, and you really don't need to for the explanations I'm presenting. The frame effects of rotation are a combination of the two, and I hope to be able to explain the overall frame effects without you needing to understand the math.

Back to the Main Coriolis force Page.