Intermediate Axis Theorem.... fun to learn it again with You Tube

[CPW]

A friend of mine shared a YouTube video with me, saying he was sure I would love it. He described it as very strange with a rotating wingnut in the space station flipping over on its rotation axis, over and over, while it spun rapidly.

After watching the video, I verified I was taught the intermediate axis theorem in my undergraduate physics mechanics class.

Grabbing my ping pong paddle from my basement, I have been entertained by attempting to flip the racquet about the intermediate axis and had fun showing my family. You might too enjoy this topic.

 

[Klystron]

I learned a bit about these theorems while practicing knife throwing. You throw a knife nearly the same as throwing a baseball or cricket ball; use your hand, arm and wrist to power the flight and your fingers to spin the ball or blade. Balls have spherical symmetry but knives have three distinct rotational axes.

The knife thrower cares primarily about rotation of the longest axis of the knife vertically aligned with direction of flight, rotating at an origin roughly 3cm along the blade measured from the interior end of the haft (handle) for a 20cm knife. This rotation origin corresponds to the knife's center of gravity (cog). The amount of rotation imparted to the knife, measured in 1/2 turns, depends on the distance to the target. When the knife is grasped by the blade, one half turn represents the shortest flight distance to strike point first.

A typical throw covers a distance of 9m (10 yards) in 1.5 turns, ending point first in the target. The throw begins in the hips, travels down the throwing leg and arm, continues with the 'flip' or rotation imparted by the fingers at release as the arm points toward the target, and finishes with a distinct follow through motion of the hand, arm and entire body much like a pitcher.

 

[Hornbein]

Here's an application of the theorem from the Le Mans automotive racetrack.

 

[Klystron]

I guess this idea deserves a vid. This clip from wiki shows an overhand axe throw but the same principles apply.

Axe throwing in slow motion

Notice the rotation along the longest axis for stability in flight and the exaggerated follow through of the entire body