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I'm trying to figure out what effect does the rotation point where you choose to hold a drumstick have on the rebound of the stroke. Drummers usually find this point by feel, or by fiding out at which rotation point the stick produces the most rebounds. I'm curious to know what are the physics behind this.

So far I've tried to look at this problem as a straight rod with a lenghthlcertain massmand volume falling freely in a rotational movement to the rebound surface from an angleα≤15°. The distance from the mass center of the stick to the rotation point isd. I chose a small angle, so that I could assume the torque on the stick, given bym*g*d*cosαremains constant throughout the motion, thus yielding a constant angular acceleration ε, just to make life easier.By changing the rotation point, it is clear that the moment of inertiaIof the stick also changes, being lowest at the center and highest at the very end of the stick.

At first I thought that the stroke with the highest kinetic energy at the collision point (E=0.5*I*ω^{2}, where ω - angular acceleration) would yield the best rebound, but I did some calculations and found that the kinetic energy of the stroke is the greatest when the stick rotates about the very end point, and I know from practice that that's not the best place to hold the stick.

So then thought - what else has a role in the rebound? I tried to think of the rebound as just having a dampening effect of the total energy of the stick (that it takes away, for example, 10% of the total energy), thus after the rebound the angular velocity is reduced and the same acceleration ε slows down the movement of the stick. Then I tried to calculate the greatest angle travelled after the rebound, but the results made no sense - it was the same angle for all rotation points.

So, in the end, my question is - what forces play a role in the rebound of the stick? What am I missing? Should I think of the rebound surface as a spring, perhaps?

I hope I posted this in the right place.

Thank you!

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# Drumstick rebound

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