Figure skaters are used as classic examples for angular momentum. A skater enter

Question

Figure skaters are used as classic examples for angular momentum. A skater enters a spin with her arms extended out horizontally. The size and weight of her legs keep her from spinning beyond a certain speed. She gets herself spinning as fast as she can, and then she draws her arms in to their chest.

Her arms are 5kg each. When outstretched, they behave much like a horizontal thin rod 1m long. The rest of her body is about 50kg, and has roughly the same moment of inertia as a cylinder 15cm in diameter.

If she starts off going 60rpm, how fast will she be spinning when she pulls in her arms?

Explanation / Answer

initial condition:

when the arms are outstretched.

then moment of inertia of the hands around the axis passing through the center of the arm=(1/12)*mass*length^2=0.4167 kg.m^2

but as she is spinning around the center of her body, the axis is at a distance of (1/2)+(0.15/2) m from the present axis

(here we have considered the distance of the center of the thin rod from the axis passing through the center of the cylinder , by which her body is modellled..so net distance will be half of the length of the thin rod+radius of the cylinder)

distance=0.5+0.075=0.575 m

so net moment of inertia=0.4167+mass*distance^2=2.0698 kg.m^2

similarly for the other hand, the moment of inertia will be 2.0698 kg.m^2

now for her body, the moment of inertia will be 0.5*mass*radius^2=0.141 kg.m^2

so net moment of inertia of her total body=2.0698*2+0.141=4.2806 kg.m^2

case 2:

when she pulls her arms in,

moment of inerta=0.5*(50+5+5)*(0.15/2)^2=0.16875 kg.m^2

so using conservation of angular momentum,

4.2806*60=0.16875*w

w=1522 rpm

Related Questions

Navigate

• Browse (All)
• Browse F
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.