We explore the changing velocity of a pole dancer's spin using a pole which rotates as the performer spins. Assuming the motion is frictionless we find that an initial leg whip perpendicular to the pole lasting pi radians results in a velocity of 0.484 rev/s. By pulling the outstretched leg in to the pole the velocity increases massively to 7.74 rev/s

Doherty, Lauren

Kamran, Aneesah

Rhodes, Kira

English

University of Leicester Open Journals

Journal of Physics Special TopicsAn undergraduate physics journalS3 6 Spinning AroundK. Rhodes, L. Doherty, A. KamranDepartment of Physics and Astronomy, University of Leicester, Leicester, LE1 7RHNovember 16, 2017AbstractWe explore the changing velocity of a pole dancer’s spin using a pole which rotates as the performerspins. Assuming the motion is frictionless we find that an initial leg whip perpendicular to thepole lasting pi radians results in a velocity of 0.484 rev s−1. By pulling the outstretched leg in tothe pole the velocity increases massively to 7.74 rev s−1.IntroductionIn pole fitness a spinning pole has an outercylinder which rotates around an inner cylinderso that the pole moves with the performer. Thisset up is virtually frictionless and it’s possible tocontinue spinning for a long time without slow-ing down. In this paper we look at the change ofangular velocity of a climbing spin on the pole.In this move the pole dancer’s leg whip createsthe torque which drives the spin. In an idealscenario, to generate the maximum angular mo-mentum, this leg is perpendicular to the pole asit is whipped around as shown in Figure 1.Figure 1: Diagram showing the leg whip for a climbingspin where the arrows show the moment arm r.TheoryWe study the motion of the climbing spin byfirst finding the angular velocity ω after the legwhip then at the maximum angular velocity withthe leg pulled in to the pole. The equationfor constant angular acceleration used is Eq. 1where the initial velocity ω0 is zero [1]ω2 = ω20 + 2α∆θ. (1)The variable ∆θ is the angle passed through bythe outstretched leg and α is angular accelera-tion. We find the acceleration of the whip usingEq. 2 rearranged for α:τnet = Iα, (2)and using the definition of torque τ (the force Ftimes the radius of the axis of rotation r) andthe moment of inertia I. We estimate the mo-ment of inertia for the pole dancer by modellingthe leg whip as a cylinder as shown in Figure 1which gives I as mr2. Combining the two previ-ous equations we reach Eq. 3 which isω =√2τnet∆θ/I =√2F∆θ/mr, (3)where F is the force of the leg whip.The maximum angular velocity of the poledancer is found by using the conservation of an-gular momentum L, given in Eq. 4,L = mr2i ωi = mr2fωf , (4)where ri and rf are the initial and final radiiand ωi and ωf are the initial and final velocities.The mass m is constant and disappears when theequation is rearranged for ωf .ResultsNeglecting drag, the force contributing to thetorque of the spin is equivalent to the weight ofthe dancer’s leg. This is because the leg is per-pendicular to the axis of rotation and so sin θis zero. The weight of the leg is approximatedby using that a leg is approximately 18% of themass of a woman’s body [2]. We assume thepole dancer’s mass m is 60 kg which gives us aleg mass of 10.8 kg, or leg weight F of approx-imately 106 N. The moment arm r is estimatedas 1.2 m and the angle travelled through in theleg whip as pi (180 degrees). Using Eq. 3 we findthe angular velocity of the leg whip to be 3.04rad s−1 or 0.484 rev s−1.We find the maximum velocity of the spinwhere the pole dancer’s leg is pulled into the poleand we estimate the new moment arm rf to be0.3 m. We rearrange Eq. 4 for ωf and use ωias 3.04 rad s−1 and the initial moment arm rias 1.2 m. The new velocity of the pole dancer is48.6 rad s−1, which is 7.74 rev s−1 which is 16times the revolutions per second for the initialleg whip. This is much higher than we expectedand in reality the velocity would not reach suchhigh velocities due to friction and taking into ac-count the mass of the pole. In addition a perfectspin would have to be performed to reach thisvelocity. These factors have all been neglectedin this ideal scenario.ConclusionWe found the changing angular velocity ofa spinning climb on a spinning pole using thetorque used to drive the spin and constant an-gular acceleration equations. By modelling thepole dancer’s movement around the pole as acylinder with constant mass along the momentarm, the moment of inertia could be estimated.Using this we found the angular velocity reachedas 3.04 rad s−1 or 0.484 rev s−1. Through thepole dancer pulling their leg close to the polewe found the maximum angular velocity reachedwas 48.6 rad−1 or 7.74 rev s−1 which would beunlikely to reach in reality but makes sense withour assumptions.References[1] Tipler, P. (2008). Rotation and Angular Mo-mentum. In: Marshall, C. Physics For Scien-tists and Engineers. Basingstoke: W.H. Free-man and Company. p317, p354.[2] Plagenhoef, S. (1983). Anatomical Data forAnalyzing Human Motion. Research Quar-terly For Exercise and Sport. 54.

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S3_6 Spinning Around

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