Measure the Length of a Moving Rod

**Material**

A toy vehicle that moves at a constant slow speed, (For Example 5 seconds per meter.)

A rod (for example 0.5 m long)

A meter stick or two

String at least 1 m long

Sticky tape

Three people

**Assembly**

Tape the string between the vehicle and the rod. The vehicle will drag the rod as it moves.

A blue car uses a string to pull a brass rod next two two meter sticks.

**To Do and Notice**

Measure the length of the rod when it is at rest.

Now place the meter stick or two on the table.

Place one end of the rod near but not at the zero end of the meter stick(s).

Have one person measure the position of the front of the rod, and the other person measure the position of the back of the rod.

Subtract the two positions and find the rest length, or proper length, of the rod. L0.

Notice that the measurements can be made at any time and produce the correct length of the rod.

You will now measure the length of the moving rod.

Plan your measurements ahead: one person will measure the position of the front of the rod while a second person will measure the position of the back.

The two people may communicate.

A person starts the car pulling the rod and then one other person measures the position of the front while another person measures the position of the back.

Notice that both measurements must be synchronized to occur at the same time in order to produce the correct length.

The person measuring the front position can call out so that the person measuring the rear makes the measurement at the same time.

Subtract the readings to find the length of the rod.

A Relativistic Measurement

In relativity, two events that are synchronized in one frame of reference will not be synchronized in a moving frame of reference.

Now measure the length of the rod by having the front person call out when they make their measurement, and then have the rear person wait two seconds before making their measurement.

What is the measured length of the rod now?

By having the people measuring the rear location wait two seconds after the people measuring the front the rod will have moved.

The measured length of the moving rod will be less.

This is why there is length contraction in relativity.

**Going Further**

How long is the moving meterstick?

The two people must not communicate once the stick has started moving.

Use two stopwatches to coordinate the two measurements.

A box can be placed over the rod so that the front team cannot see the back team's measurement.

The problem here is that the stopwatches must be synchronized.

And the observers must agree at what time the measurements will be made.

The person measuring the front of the meter stick can instruct the third person when to start the pulling vehicle.

A box may be placed over the rod so that the people making front and back measurements cannot see each other.

**So What?**

A relativistic ally moving observer disagrees with a stationary observer about whether events at different locations are simultaneous or not.

An observer riding along with the moving meter stick will measure the rest length of the meter stick.

An observer measuring a relativistically moving meter stick will measure its length to be shorter than its rest length.

The stationary observer will say that this is because the observer of the moving stick measured the position of the front and the rear at different times.

The observer of the moving stick will disagree and say that the positions were measured at the same time.

Events which are simultaneous in one frame are not simultaneous in a moving frame.