Kinematics Notes

Relative Speed

[Chapter 2 Objectives]

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At this point you may be thinking that average speed is a pretty simple-minded idea. OK, what's the answer to the question above - what is it like to go 1,000 mi/hr? Extreme vibration - unbearable noise - huge forces pushing you back in your seat - face distorted - that sort of thing, right? What is the fastest that you have ever gone?

What is your average speed right now? Probably your answer is 0. Sure, you are sitting at your computer, you move 0 meters (or feet or miles, or whatever), so your average speed is 0 meters divided by any time at all = 0 m/s (or 0 mi/hr, etc.)

Suppose, however, that a person were in a spacecraft hovering over the Earth's North Pole, and they want to measure your average speed. The earth makes one complete revolution on its axis in 24 hours, so the distance you move (since you are attached to the earth) equals the circumference of the earth, which is about 25,000 miles. Your average speed, therefore, equals 25,000 miles divided by 24 hours, or a little over 1,000 mi/hr!

So, what's it like to go 1,000 mi/hr? It's like this! You are going 1,000 mi/hr right now!

Actually, 1,000 mi/hr is peanuts! Suppose that a space traveler were hovering over the Sun right now, and they wanted to measure your average speed. You (since you are attached to the Earth) are revolving around the Sun, and you will complete one revolution in a year. The distance that you go in that time equals the circumference of the Earth's orbit. The radius of the Earth's orbit is about 93 000 000 miles, so the circumference of the orbit is about 6 (2 pi) times 93 000 000 miles... Your average speed right now is about 66 000 mi/hr! (Check the calculation.)

By the way, the Sun is revolving about the center of the Milky Way Galaxy...

Right now, you are probably thinking that this is some kind of a
trick - you are **really** going 0 mi/hr, and the 1,000
mi/hr and 66,00 mi/hr calculations aren't really your **true
speed**. I have some shocking news for you!

Whenever you measure speed, you have to "stand somewhere" to make
the measurements. In other words, you must consider some object (the
one you are standing on, probably) to be at rest, and measure the
speed of other objects *relative to it* - that is, as if it
were at rest.

When we measure speeds, we commonly stand on the Earth (or
something attached to the Earth) to make the measurements. A
physicist would say that the speed is measured *relative to the
Earth* or in the *Earth frame of reference*. Notice that
it is quite useful and consistent to treat the Earth as if it were at
rest - even though we know that it really isn't at rest at all!

The space traveler hovering over the North Pole of the Earth sees you (attached to the Earth) moving and considers herself at rest. Her speed measurement is made relative to her position in space. Her speed measurement is also quite useful and consistent (for her) - NEITHER MEASUREMENT CAN BE CONSIDERED THE CORRECT OR TRUE SPEED!

Isaac Newton, among other prominent physicists, believed that even though the speeds that we commonly calculate are always relative quantities, that there had to be somewhere in space that was truly, absolutely at rest, and that, at least theoretically, true speed measurements could be made relative to that spot. Now we know that this is not true - all speeds are relative.

The textbook says "motion is relative" but that is a little too vague, because *everything* about motion is * not* relative. We can say, though, that the positions, speeds, and velocities of objects

Suppose that Abe and Betty are riding in a car on a long straight road - Abe is in the back seat, and Betty is in the front seat. Charlie is standing beside the road.

Suppose that Charlie notices that the car takes 5.0 seconds to
move between 2 marks on the road that Charlie has previously measured
to be 40 meters apart. Charlie calculates Betty's speed (Betty is in
the car, remember) as 40 m/5.0 s = 8.0 m/s *relative to
Charlie* (or *relative to the Earth*).

During this same 5.0 seconds, Abe observes (Abe is also in the
car) that Betty has remained motionless - he calculates Betty's speed
as 0.0 m/5.0 s = 0.0 m/s *relative to Abe* (or *relative to
the car*).

So, which is Betty's *"correct"* speed - 8.0 m/s or 0.0
m/s? For Abe, Betty, and Charlie to argue back and forth about it
would be pretty silly - **both speeds are correct**.
They are both perfectly sensible, consistent, and useful - in their
own frame of reference.

You may want to study the motion of a projectile cart. It shoots a ball straight up using a spring-loaded "cannon." When the cart is at rest, the ball comes straight back down into the cannon, but when the cart is moving at a constant velocity, the ball still lands in the cannon! Why? Because velocities are relative! Try it!

The fact that speeds are relative has some important and
interesting consequences. For instance, if you (and I) are really
going 1 000 mi/hr right now (in some frame of reference), it must be
**impossible to tell how fast you are going without reference
to some other object**. In other words, if you were locked in
a box with no windows or doors, *there would be no experiment you
could perform to tell how fast you were going*. Since all speeds
are relative - there is no *"true speed"* - this means that,
in some sense, speeds aren't real. At least, speed is not a truly
fundamental physical quantity.

This discussion might remind you of the *Theory of
Relativity* - for good reason. What we have been discussing is
often called Galilean (or Classical) Relativity. I don't want to get
into Einstein's Relativity right now - except for one thing. Einstein
did **not** say "everything is relative" - everything is
**NOT** relative. Only the things that are not truly
fundamental are relative.

More on Relative Speed (AP)

[Chapter 2 Objectives]

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last update January 19, 2009 by JL Stanbrough