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# Rotational dynamics

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A turn-table on a frictionless vertical axis has a radius of 1.5 m and a moment of rotational inertia of 150 kgm^2. It is at rest until a 75 kg person who had been standing still (and who can be treated as a point), begins to walk around the rim at a speed of 2.0 m/s with respect to the turn-table.
a) what is the speed of the person with respect to the Earth?
b)How much work did the person do in bringing the turn-table up to speed?

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#### Solution Preview

Please see the attached file for answer
a) what is the speed of the person with respect to the Earth?
Moment of inertia of turntable= 150 Kg m^2 =It

Radius of turntable= 1.5 m
Mass of the person= 75 Kg
"Moment of inertia of the person with respect to the vertical axis=
M r ^2 =" 168.75 Kg m^2 =Ip

Let the person be moving with angular velocity w p with respect to the earth
Let the turntable be moving with angular velocity w t with respect to the earth

w p= Vp/r where Vp is the velocity of the person with respect to the earth
w t= ...

#### Solution Summary

Calculates the speed of the person with respect to the Earth and the work the person did in bringing the turn-table up to speed.

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