Question

A horizontal disc rotates about an axis which passes vertically through the center of the disc with angular velocity of 100 r.p.m. A small particle of mass 10g is dropped onto the disc 9.0cm from the axis and sticks to the disc. If the angular velocity is reduced to 90 r.p.m. Determine the moment of inertia of the disc about the axis.

Answer 1

To find the moment of inertia of the disc about the axis, one can apply the conservation of angular momentum before and after a particle sticks to the rotating disc.

Step-by-step explanation:

to a rotating horizontal disc, its moment of inertia changes due to the redistribution of mass around the axis of rotation. Initially rotating at 100 revolutions per minute (r.p.m.), the disc's moment of inertia is calculated using the mass, distance from the axis, and initial angular velocity. Employing the conservation of angular momentum principle, the initial moment of inertia is determined. Afterward, as the angular velocity decreases to 90 r.p.m., the conservation of angular momentum is applied again to find the new moment of inertia. The change in angular velocity leads to a corresponding alteration in the moment of inertia to conserve angular momentum. Following the calculation, the disc's moment of inertia after the change in angular velocity is approximately 0.000270 kg⋅m².