Linear Momentum ; Kinetic Energy; Rotation; Speed An Olympic figure skater havin

Question

Linear Momentum ; Kinetic Energy; Rotation; Speed

An Olympic figure skater having a mass of 48 kg glides across the ice at 2.8 meters/second. What is her linear momentum? What is her kinetic energy? Then, she leapt end lands on the foe of one skate, twirling into a graceful pirouette, with her arms held tightly together straight up over her head. As an engineer, you know she has merely converted translational motion into rotational motion. If her body can be modeled as being a circular cylinder with a radios of 0.32 meters, how many rpm (revolutions per minute) is she rotating? She then fully extends her arms, straight out from her shoulders. Assume her arms can be modeled as slander bars, each 0.65 meters long and having a mass of 5 kg Whet is her new rotational speed in rpm?

Explanation / Answer

Linear momentum = mv

                                = 48 * 2.8 = 134.4   kg.m/sec

Kinetic energy = 1/2 * 48 * 2.8 * 2.8 = 188.16 J

Here, 1/2 * I * w2 = 188.16

=>       1/2 * (1/2 * 48 * 0.32 * 0.32) * w2 = 188.16

=>   w =   12.374   rad/sec

=>    she is rotating at = 118.22   rev/min

Applying conservation of angular momentum

=>    (1/2 * 48 * 0.32 * 0.32) * 118.22   =   (1/2 * 48 * 0.32 * 0.32 + 2/3 * 5 * 0.85 * 0.85) * w

=>   w   =   60 rev/min

=> new rotational speed =   60 rpm

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