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On the bus

Jacky is sitting on a moving bus.

Is Jacky moving?

You the student: “Well of course he is! Jacky is moving because the bus is moving!”

Ok, then what if we were all sitting on the bus with Jacky? I ask you, “Hey, I’m a little creeped out, is Jacky moving [closer to us]?”

You say: “of course not! He’s sitting on the bus!”

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Which answer is correct?

Is Jacky moving or not!?

It depends on:...

WHO YOU ASK!

Speed is relative or its value depends on where it is observed and measured.

This is known as:

Frame of Reference

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Example 1

A bus travels at 15.0m/s

If a person on the bus gets up from the back and walks to the front at 1.2 m/s, what is their speed relative to �a) someone standing on the street?

a) 15m/s + 1.2m/s = 16.2m/s

If another person on the bus gets up from the front and walks toward the back at 1.4m/s, what is their speed relative to �

b) someone standing on the street?

b) 15m/s + (-1.4m/s) = 13.6m/s

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Similar to a moving walkway

The people only appear to be moving to us because we are not on the walkway and are watching from the window’s frame.

Ever tried to walk the opposite way at the same speed? You go have zero speed from the perspective of the window.

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General equations to describe

So we write: u = v + u’

u = vel observed from rest frame�(in this case, you)

v = velocity of the moving frame�(the bus)

u’ = velocity observed from the moving frame (inside the bus)

OR: u’ = u - v

Similarly:

If we multiply every term by t: we get

u't = ut – vt

Let x’ = distance measured in the moving frame.

x’ = x - vt

How far I moved inside the bus = how far the street person saw me move - how far the whole bus moved.

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Testing movement.

So even though you sit here reading these notes, can you tell you are moving ?

Of course you are moving! You’re moving relative to other reference frames!

Is there an experiment you could do to check if you’re moving?

Think about sitting in a uniformly moving car. (constant velocity)

If you toss a tennis ball to the front or back or straight up has the motion changed because the car is moving?

According to the sun, you are moving at

29.77km/s

RIGHT NOW!

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So what?

The answer to the tennis ball question is no. It doesn’t matter if the car is moving. The tennis ball will not behave in weird ways.

If I jump up right now, I do not slam into the wall because the earth is rotating!

That brings us to….

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THE FIRST POSTULATE OF SPECIAL RELATIVITY!

(You’re all moving right now according to someone’s reference frame, you just can’t tell.)

The laws of physics are the same in all

uniformly moving frames of reference.

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