In breakdancing, a headspin is a basic power move (a move requiring tremendous strength to complete). Headspins are performed by engaging in a handstand, then lowering the body such that the head touches the ground. The breakdancer then lifts their hands and pushes off, causing rapid spinning on his or her head. The breakdancer stretches their legs as in the splits. By contracting or extending his or her legs, a breakdancer can make a headspin go faster or slower, respectively. This relies upon angular momentum and moment of inertia. Momentum measures how likely an object will change in position along a straight path at constant speed. Angular momentum measures how likely an object will spin. It correlates the mass and speed of the object to the radius of the circular path. Angular momentum is constant unless torque is applied. It can be used to measure torque applied to an object over time based upon differences between initial and final angular momentum. In the case of a breakdancer, there is a friction force decelerating the headspin.
The formula for angular momentum (L) is:
L = mass x velocity x radius
The formula for linear momentum (p) is:
P = mass x velocity
The radius is the distance from the point around which the object spins. In the case of a breakdancer with legs fully extended, this would be the distance from between his or her crotch and toes. For an object with constant mass rotating in a constant path, the angular momentum is the product of the object's moment of inertia and its angular velocity vector. I is the moment of inertia of the object and Ï‰ is the angular velocity.
L = I x Ï‰
If somebody is 60kg and 1.8m tall, then their legs are approximately .9m long. This means that the breakdancer will have a diameter of 1.8 m from the tip of one toe to another. This problem will describe the motion of a breakdancer performing a headspin for 1.5 seconds. The coefficient of kinetic friction between leather and steel is .6, so this problem will assume the coefficient of kinetic friction between a scalp and a linoleum floor is .4.
Friction causes a decelerating force of:
F = 60 x 9.8 x .4 = 235.2N
Therefore, it decelerates a breakdancer by:
235.2N = 60 x a
a = 3.92m/s2
In order to remain in motion for 1.5 seconds, the breakdancer must therefore begin with a velocity of:
0 = vxi + 3.92 x 1.5
vxi = 5.88m/s
The angular momentum will be:
L = m x r x v = 60 x .9 x 5.88 = 323.52 kgm2/s
If the person bends their knees to cut split the length of their legs, then their radius is cut in half. As a result, their velocity doubles to become 11.76 initially. Friction will require the breakdancer to eventually apply more fore to maintain high speed. However, by pulling in his or her legs the breakdancer will be able to move faster with much less force. This is due to angular momentum.
So, by decreasing radius, linear momentum increases to maintain a constant angular momentum. Since the person does not get significantly fatter while breakdancing, their velocity must increase to accommodate a constant angular momentum.