## Saturday, November 11, 2017

### You + Hula Hoop = Physics!

Who doesn't love hula hooping?
Me.
So in the hopes of improving my skills, let's study it!
Keeping the hula hoop on a person's waist and maintaining its circular movement requires forces acting upon the hoop. The friction between the hula hooper and the hoop keeps the hoop positioned on the person's waist; this friction also causes the hoop to slow down as it brushes against clothing. The hula hooper's hips exert an upwards force on the hoop, which opposes gravity and also serves to maintain its position. The person also produces torque from the hips, which is an outward turning force required to maintain the centripetal force of the hoop; without this, the hoop would fall to the ground.

When a person steps inside of a hula hoop, he or she becomes the hoop's axis of rotation (denoted by the hoop's radial symmetry). The individual must perform work by moving his or her hips to maintain the hoop's momentum created by the initial spinning of the hoop. According to angular momentum, it is less challenging to keep a heavier hula hoop moving than it is to maintain a light hoop's movement, as long as the hoops' radii are constant. This is because the hoop's angular momentum is directly related to the hoop's mass. When we consider the hula hooper to be a point mass, then angular momentum can be quantified by:
L=rpsinθ                                        where p=mv
If we consider the hula hooper a continuous object, the principle still holds:
L=Iω                                              where I=mr and ω= Δθ/Δt
So those hula hoops with the sand in them? Turns out the extra weight of the sand is intended to help challenged hula hoopers like myself keep the hoop moving! If we increase the radius of the hula hoop, we would need to spin it faster (to achieve the same change in angle over time) in order to maintain the same momentum as a hula hoop with a smaller radius. This can also be seen in the angular velocity formula, in which the radius is inversely proportional to velocity:
v=rω
Moral of the story? If you struggle with hula hooping like I do, buy a weighted hoop with a small radius so you have a chance at hula hooping success.

Sources
https://www.scientificamerican.com/article/bring-science-home-hula-hoop-physics/
https://people.howstuffworks.com/hula-hoop1.htm