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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.

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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.

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

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