Making Rotating Arms

Let us make ‘rotating arms’ using two paper straws and a paper clip by following these steps:

(1) Take two paper straws and a paper clip.

(2) Insert the straws into the arms of the paper clip.

(3) Your rotating arm is ready!

Make several ‘rotating arms’ with different angles between the arms. Arrange the angles you have made from smallest to largest by comparing and using superimposition.

Passing through a slit: Collect a number of rotating arms with different angles; do not rotate any of the rotating arms during this activity.

Take a cardboard and make an angle-shaped slit as shown below by tracing and cutting out the shape of one of the rotating arms.

Now, shuffle and mix up all the rotating arms. Can you identify which of the rotating arms will pass through the slit?

The correct one can be found by placing each of the rotating arms over the slit. Let us do this for some of the rotating arms:

Case 1: Slit angle is greater than the arms’ angle. The arms will not go through the slit.

Case 2: Slit angle is less than the arms’ angle. The arms will not go through the slit.

Case 3: Slit angle is equal to the arms’ angle. The arms will go through the slit.

Only the pair of rotating arms where the angle is equal to that of the slit passes through the slit. Note that the possibility of passing through the slit depends only on the angle between the rotating arms and not on their lengths (as long as they are shorter than the length of the slit).