Sunday, 8 May 2011

Relative motion!

Now when we have setted up the stage for motion of matter and defined basic laws we can start to looking at interesting property of motion.
You may have noticed how rolling wheel looks like: upper part seems to be moving fast, while lower part is almost stationary. Is it some sort of an illusion? Not at all! The highest point of wheel moves twice as fast as whole wheel, while the ground touching point does not move! How can it be so?

To investigate this problem, you can do a simple experiment. Just fix something well visible (like a ribbon) on bicycle wheel and let someone to ride with it. What trajectory of the ribbon do you notice? It should look something like that:
 Picture from excel simulation found in Jon Peltier's blog. You can download it from here

You should have noticed that 'ribbon' moves much faster at the upper part of the wheel, compared to the lower part. Why does it happen so? 
The answer appears to be very simple. Rolling of a wheel consists of two distinct motions: rotation around the axis and straight movement of whole wheel. Hence the resulting velocity by principle of relativity is just the sum of both (in the ground frame of reference).

Using this, can you see how the speed at the point touching ground is zero (but acceleration is not zero), while the most upper point is moving twice as fast as whole wheel?

Did you know that some parts of a train moves backwards as train moves forwards? Train wheel looks like that:

Since whole wheel is rotating with the same angular speed, then speed at any part of the wheel is .
Which means, that farther from centre you are, the greater your speed is. 
This means, that on the train wheel point C is moving faster then whole train. Thus by principle of relativity, sometimes point C will be going to different direction, compared with the direction of the train motion.

This can be illustrated by animation created by Jon Peltier:

From this you can see that some parts of the train moves backwards sometimes. 
For those who are interested for more details, check here.

Curiously, same considerations can be applied for a moving and rotating earth. When do you move faster around the Sun, at day or night? Strange questions, huh? Let's look to the Earth from somewhere close to the North start:
Adapted from

As you can see from the picture, people at night move faster around the sun. Somewhere around the equator the difference between relative orbiting speeds around the Sun at midnight and midday is approximately 1km/s which is rather fast. However, earth rotation speed close to equator is only 1.5% of average speed of orbiting the Sun, thus this effect is hardly noticeable.

When looking to the stars, we perceive their position, by direction of light coming at us. But since we are orbiting the Sun, we will perceive light coming from a bit different direction because of the vector sum of velocities. Although our orbiting speed is very slow compared to the speed of light, we still can notice difference in direction using modern equipment. Such effect is called astronomical aberration of light.

Imagine an old style duel: two persons are standing in front of each other and is trying to shoot each other with a gun. All this crazy action takes place in a moving ship. One person stands at the front of the moving ship, another one stands at the end. However the second one protests that conditions are unequal. Assuming that there is no relative air movement (wind), would you consider second person being right?

Relativity is very important idea in understanding of the world. However it is also very important in our lives. All our perceptions are relative. Do you notice it? Challenge attitudes of yourself and people around you. Who is tall who is small, who is poor who is rich, who is smart who is dumb? Compared to what? We would not know happiness if we would not have been unhappy sometimes...

Have you noticed or not, but we have just explored outstanding phenomena of space and time called relativity. Principle of relativity is very fundamental. Because of it there are conservation laws. The principle of relativity states that laws of physics are the same in all inertial frames of reference. If theory of Electromagnetism is right, speed of light must be the same in inertial frame of reference. This leads to theory of special relativity. To see how strange it is watch this:

1 comment:

  1. George Carlin mentions relativity in everyday life :)