A child of mass 21 kg stands at the center of a platform of radius 2.0 m and rot

Question

A child of mass 21 kg stands at the center of a platform of radius 2.0 m and rotational inertia 670 kg*m2. The circular platform rotates about a frictionless shaft with an angular speed of 1 rad/s. The child walks along a radius until it reaches the rim.

1) What is the angular speed of the platform when the child reaches the rim?

2) What is the difference in energy between the final and the initial energy of the child plus the platform? (Determine for yourself where the work that made this change comes from).

Explanation / Answer

from the conservation of angualr momentum

Li= Lf

Ii wi = If wf

wf = wi I i/ If

= 1 rads/ ( 670)/670+(21)( 2)^2

=0.88 rad/s

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(2)

Ki = 1/2*I*^2 = 1/2*670*1^2 = 335 J

Kf = 1/2*I*f^2 = 1/2*(670 + 21(2)^2) *0.88^2 = 291.94 J

del K = Kf-Ki = -43 J

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