On average, both arms and hands together account for 13 % of a person's mass, while the head is 7.0 % and the trunk and legs account for 80 % . We can model a spinning skater with her arms outstretched as a vertical cylinder (head, trunk, and legs) with two solid uniform rods (arms and hands) extended horizontally. Suppose a 70.0 kg skater is 1.50 m tall, has arms that are each 66.0 cm long (including the hands), and a trunk that can be modeled as being 33.0 cm in diameter. If the skater is initially spinning at 69.0 rpm with her arms outstretched, what will her angular velocity ω 2 be (in rpm ) after she pulls in her arms and they are at her sides parallel to her trunk? Assume that friction between the skater and the ice is negligble.

Her angular velocity is 439.41 rpm

Explanation:

The moment of inertia when her arms are at her side is

Where m=70 kg, r=33/2=0.165 m

The moment of inertia when her arms are stretched out is

Where L=66 cm=0.66 m

mb= mass of body except hands=0.87*70=60.9 kg

mh= mass of hands+arms=0.13*70=9.1 kg

The conservation of angular momentum is:

Li=Lf

Ii*wi=If*wf

Clearing wf:

Replacing values:

this is poiselle's equation from fluid mechanic in physics. mech eng

the total distance that martina travels that day is

(distance from home to mom's office) plus (distance from mom's office to school)

plus (distance from school to library) plus (distance from library to friend's house)

plus (distance from friend's house to martina's house).

(we don't know what any of these distance actually is.)