## Tuesday, October 30, 2012

### THE PHYSICS OF A LONG BACK SPINGING KICK

A long back spinning kick is a kick where the practitioner (me.) spins using the foot that is initially behind them to kick in a circle by raising their foot at they go. The kick is intended to hit the target 180° after motion has started.
* Please note this is actually not a circle it is an oval because I have to shift my weight as I go, but for this problem we’re going to call it a circle.
I know that I can kick hard enough to break someone’s ribs. It takes 3300 newton’s to do this (the average martial arts master can, depending on the kick, get up to 9000 newton’s.) I’m not a master and I’m pretty small so let’s just stick to breaking a rib here. So torque is:
T=rFsinΘ
Where Θ is 90. The length of my leg is about .69m and since I’m pivoting in a circle the distance to my foot is the radius. So the torque is going to be
.69*3300*sin90
Torque is 2277 Nm.

Now to get the Radial Acceleration we use the equation T=Iα if we assume my leg is a thin straight object with the point that we rotate around being the end. Than the equation for torque should read. T=[(mL^2)/3]*α.
Now I have a mass of 50 kilograms. (well 49.8 but let’s call it 50.) And my leg to my hip joint is about .69m. And earlier we found the torque to be about 2300Nm so we get
α=(T*3)/(ML^2)
α=(2300*3)/(50*.69^2).
α=23.8m/s^2
So to get the angular velocity of my foot at the point of contact.
α=ω/t.
So I timed myself kicking and it takes me.75 seconds for a half a circle. Because we assume once I hit the guy I stop spinning.
ω=αt
23.8*.75=ω
ω=17.9 m/s.
So in order to get the linear velocity my foot hits the target with we take the angular velocity and times it by the radius.
V=ωr
17.9*.69=V
V=12.35m/s.
To give you a better reference for this number 12.35m/s is 27.63mph.