A 58.0-kg woman stands at the western rim of a horizontal turntable having a mom

Question

A 58.0-kg woman stands at the western rim of a horizontal turntable having a moment of inertia of 480 kg·m2 and a radius of 2.00 m. The turntable is initially at rest and is free to rotate about a frictionless vertical axle through its center. The woman then starts walking around the rim clockwise (as viewed from above the system) at a constant speed of 1.50 m/s relative to the Earth. Consider the woman-turntable system as motion begins. (a) Is the mechanical energy of the system constant? No (b) Is the momentum of the system constant? Yes No (c) Is the angular momentum of the system constant? Yes No (d) In what direction and with what angular speed does the turntable rotate? magnitude direction Select- rad/s (e) How much chemical energy does the woman's body convert into mechanical energy of the woman-turntable system as the woman sets herself and the turntable into motion? Need Help? Read ItMester

Explanation / Answer

mass of the woman, m=58 kg

moment of inertia, I=480 kg.m^2

radius, r=2m

speed, v=1.5 m/sec

a)

yes

because the systam experienced zero net external work

b)

yes

c)

yes

d)

by using law of conservation of angular momentum,

L_woman + L_turntable =0

Iw*Ww+It*Wt=0

mw*r^2*Ww + It*Wt =0

mw*r^2*(V/r) + It*Wt =0

mw*r*v + It*Wt =0

58*2*1.5 + 480*Wt=0

===> Wt=-0.362 rad/sec^2

angular speed of the turntable, Wt=0.362 rad/sec^2

and

direction ---> counter clock wise

e)

workdone = change in K.E

=1/2*mw*v^2 +1/2*I*Wt^2 -0

=1/2*58*1.5^2 +1/2*480*0.362^2

=96.7 J

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