What is proper length?

State the length contraction formula.

Which length is larger, \(L_0\) or \(L\), for a moving object?

A rod has proper length \(10.0\,\mathrm m\) and moves with \(\gamma=2.00\). Find its measured moving length.

A rod moves at \(0.600c\). Find \(\gamma\).

A spacecraft has proper length \(100\,\mathrm m\) and moves at \(0.800c\). What length does Earth measure?

A moving object is measured to be \(4.00\,\mathrm m\) long. If \(\gamma=1.25\), find its proper length.

Why must the two endpoints of a moving object be measured simultaneously in the observer's frame?

A rod has proper length \(6.00\,\mathrm m\) and is measured as \(3.60\,\mathrm m\). Find \(\gamma\) and the speed.

A meter stick moves at \(0.900c\) parallel to its length. Find its length in the lab.

A square plate moves parallel to one of its sides at \(0.800c\). Its proper side length is \(2.00\,\mathrm m\). What are the measured side lengths in the lab?

A tunnel has proper length \(500\,\mathrm m\). A train moving at \(0.600c\) passes through it. What tunnel length is measured in the train frame?

At what speed is a moving object's measured length half its proper length?

A rod is angled so it has a \(3.00\,\mathrm m\) component parallel to motion and a \(4.00\,\mathrm m\) transverse component in its rest frame. If \(\gamma=2.00\), find its measured length.

Explain why length contraction and time dilation are linked by simultaneity.

Derive length contraction using endpoint events simultaneous in the lab frame.

A student says the moving object physically gets crushed. Correct this interpretation.

Show that no length contraction occurs for dimensions perpendicular to the relative velocity.

A rod has proper length \(L_0\). Find the fractional contraction \((L_0-L)/L_0\) in terms of \(\gamma\).

Show that length contraction disappears in the Newtonian limit.