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The Physics Behind a Kendama

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Danny Pham

on 10 September 2014

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Transcript of The Physics Behind a Kendama

How does it move?
The movement of the Kendama can be explained by Kinematics, which describes the motion of objects!
Let’s assume a beginner picks up the kendama and doesn’t know how to do any tricks except spin the ball around the stick in a circular motion (that’s still fun!). The string has an average length of 0.40 m, and on average, the ball will make two complete revolutions every second. The distance it travels per revolution comes from the equation below, the distance it travels is a circle, so we have to use 2*pi*r.

Work follows the equation of W = F*d, where F is the force of the Kendama’s motion and D is the distance it traveled. The movement above, simply spinning the kendama in a circular motion at constant speed results in ZERO work since there is no displacement! Let’s assume the player wants to do the most basic trick, hold the kendama ball as high as possible and simply let it drop and catch it with the spike. The work done by that motion is illustrated below.
What forces are acting on the Ball?
Just before launch, only two forces are acting on the ball. Gravity (mg) and the tension within the string attached to the ball. Both forces are equal and opposite to each other since the ball is not moving.
What about torque or angular momentum?
There is even angular momentum in the kendama toy! Angular momentum is the quantity of the rotation of an object. Let’s go back to the trick where you are simply spinning the ball in a circle again. We can use that to figure out the angular momentum. The equation is as follows. L = I*angular velocity. Angular velocity is how many rotations it makes per second. (Remember I said it makes two full rotations per second! Therefore, angular velocity is 4 pi/s since 2pi is 1 full rotation). Moment of inertia is the tendency for something to resist motion.
The Physics Behind a Kendama
So What, is there physics?
Does it Move?
One of the tricks of Kendama is to propel the ball so that the cylindrical opening fits into the spike, or into the cups. So yes, it does move! It moves quite fast and beginners will often be frustrated at seeing the ball sail right over the spike and nowhere near it.

What is a Kendama?
A kendama is a Japanese toy with three cups, a ball with a hollow, cylindrical opening attached to a string, and with a wooden spike in the middle. The purpose of the Kendama is to swing the ball to land in one of the cups; one such example is to swing the Kendama so that the hollow opening of the ball will slide right into the wooden spike in the middle. See Figure 1.1 for the Kendama.

Does it Spin/Rotate?
Yes it does! As one can see from the figure, the ball rotated its orientation so that the spike can land on the spike. Furthermore, some Kendama tricks involve spinning the Kendama and letting it rotate in a circular motion to land on one of the side cups! For some tricks, it is critical so that the ball does NOT spin, so you have to work against its natural tendency to spin. So yes, there is a lot of spinning motion in the kendama toy; it is up to the player to determine if that is an advantage or not.

Well, the Kendama is a man-made object that exists in this universe. Essentially, everything in this universe follows the same set of physics. Haven’t you heard the phrase, you can’t defy physics?
Since it travels two complete revolutions every second, it travels 5 m/s.
That is its velocity. Using that information, we can also find its centripetal acceleration.
The magnitude of the centripetal force is F = m*a
That is VERY fast, but reasonable.

The amount of force makes sense. It isn’t unreasonably high or unreasonably low. It is perfectly acceptable for a 0.070kg ball.

You might be thinking, why isn’t the work gravity doing on the ball negative? The ball is allowed to simply drop and accelerate with gravity. It is not moving against gravity, so the work done on the ball is positive! If the motion of the ball was actually going up for instance, against gravity, then the work done by gravity would be negative. This is the total work done on the ball (for this particular trick) assuming that there is no air resistance or any other force acting on it.
When you just launch the ball up, gravity and torque, which is a force that cause objects to rotate, are acting on the ball. Since air resistance is very minimal, we will be ignoring it. Gravity is acting in a downward motion on the ball.
When it reaches its maximum height, gravity and tension from the ball's string both act in a downward motion.
There you go!
There are a LOT of physics involved with the Kendama toy. Isn't it fascinating to realize that physics is involved with everything we come into contact with? I hope yall learned something new!