A Solid, Uniform, Horizontal Disk with a Diameter of 2

question 57

Short Answer

A solid, uniform, horizontal disk with a diameter of 2.0 m and a mass of 4.0 kg freely rotates at 36 rpm about a vertical axis through its center. A small 0.50-kg stone is suddenly dropped onto the disk and sticks to the disk at a distance of 80 cm from the axis of rotation. The figure shows before and after views.
(a) Before the stone fell, what was the moment of inertia of the disk about its central axis?
(b) After the stone stuck, what was the moment of inertia of the system about the same axis?
(c) What is the angular velocity of the disk (in rpm) after the stone fell onto the disk?

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Definitions:

Down Syndrome

A genetic disorder caused by the presence of an extra copy of chromosome 21, characterized by physical features, developmental delays, and varying degrees of intellectual disability.

Incomplete Dominance

A genetic phenomenon in which neither allele is dominant over the other, resulting in a phenotype that is a blend of both alleles.

Recessive Gene

A gene that expresses its traits only when paired with an identical gene, as opposed to a dominant gene's traits which can manifest with only one copy.

Heterozygous Pair

A genetic condition where an individual has two different alleles of a particular gene, one inherited from each parent.