Question #20581

The dancers have identical heights, weight, and limb lengths. Assume that each dancer is in anatomical position unless stated otherwise.

Rachael is standing on her left foot. Her right leg is abducted approximately 20° at the hip. Her left arm is abducted 90° at the shoulder.

Christina is standing on her right foot. Her left leg is flexed 90° at the knee. Each arm is slightly abducted at shoulder and fully flexed at the elbow.

Melanie is standing on her right foot. Her left leg is abducted 60° at the hip. Each arm is abducted 100° at the shoulder.

Sarah is standing on both her feet. Her left arm is flexed 180° at the shoulder so it is outstretched over her head. Her right arm is slightly adducted pass anatomical position so it crosses in front of her body.

(1) Which dancer has the largest moment of inertia about her anterior-posterior axis? Why?

(2) Rank the dancer’s positions from largest to smallest moment of inertia about the longitudinal axis. Why?

(3) If each dancer is rotating with the same angular velocity about the longitudinal axis, which dancer has the greatest angular momentum about the longitudinal axis. Why?

(4) If each dancer is rotating with same angular momentum about the longitudinal axis, which dancer is spinning the fastest about her longitudinal axis? Why?

Rachael is standing on her left foot. Her right leg is abducted approximately 20° at the hip. Her left arm is abducted 90° at the shoulder.

Christina is standing on her right foot. Her left leg is flexed 90° at the knee. Each arm is slightly abducted at shoulder and fully flexed at the elbow.

Melanie is standing on her right foot. Her left leg is abducted 60° at the hip. Each arm is abducted 100° at the shoulder.

Sarah is standing on both her feet. Her left arm is flexed 180° at the shoulder so it is outstretched over her head. Her right arm is slightly adducted pass anatomical position so it crosses in front of her body.

(1) Which dancer has the largest moment of inertia about her anterior-posterior axis? Why?

(2) Rank the dancer’s positions from largest to smallest moment of inertia about the longitudinal axis. Why?

(3) If each dancer is rotating with the same angular velocity about the longitudinal axis, which dancer has the greatest angular momentum about the longitudinal axis. Why?

(4) If each dancer is rotating with same angular momentum about the longitudinal axis, which dancer is spinning the fastest about her longitudinal axis? Why?

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