# How to calculate theoretical centripetal force of a hula hoop?

I am conducting an experiment, where I will be finding the centripetal force of a hula hoop using the mass ($$m$$), period ($$T$$), frequency ($$f$$), radius ($$R$$), velocity ($$v$$), by $$v = \dfrac{2πR}T$$. By multiplying $$v$$ by $$m$$, I will be able to calculate the centripetal force.

However, in order to calculate the % error of the centripetal force, I need to calculate the theoretical force, but I am not sure what theoretical value I have to take into account in order to calculate the theoretical centripetal force.

The horizontal component of the external force coming from the hip of the person rotating the hoop must be mr$$ω^2$$ where m is the mass of the hoop, ω is the angular velocity (in rad./s), and r is measured from the center of mass of the hoop to the center of the circle in which it is moving. Since the hips are moving and are not perfect circles, r (measured to somewhere inside the person) is going to be a variable and difficult to determine. You may want to model this system with your hoop sliding around a cylinder on a friction-less horizontal plane.

• Thank you for your help, great idea! I will conduct the experiment with a cylinder instead.
– Lisa
Jul 29, 2020 at 15:09