CLASSICAL MECHANICS & THERMODYNAMICS - Chapter 5, Exercise 3 Solution
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Moment of Inertia and Angular Momentum of a Spinning Disk

PROBLEM
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A solid disk of mass 2 kg and radius 0.25 m spins with an angular
velocity of 10 rad/s. Calculate its moment of inertia and its
angular momentum. (Use I = 1/2 m r^2 for a solid disk.)

SOLUTION
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Step 1: Calculate the moment of inertia.

    I = 1/2 m r^2
    I = 1/2 x 2 x 0.25^2
    I = 1/2 x 2 x 0.0625
    I = 0.0625 kg.m^2

Step 2: Calculate the angular momentum.

    L = I omega
    L = 0.0625 x 10
    L = 0.625 kg.m^2/s

ANSWER: The disk's moment of inertia is 0.0625 kg.m^2, and its
angular momentum is 0.625 kg.m^2/s.

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WHY THIS WORKS AS AN ANSWER

The moment of inertia calculation uses the solid-disk formula from
the chapter's own reference table rather than the simpler point-mass
formula (I = mr^2), since a real disk's mass is spread continuously
from the centre out to the radius, not concentrated at a single
point - which is exactly why a solid disk's moment of inertia (1/2
mr^2) is smaller than a hoop of the same mass and radius (mr^2), as
the chapter's own text explains. Once I is known, L = I omega applies
directly, exactly mirroring how p = mv works for linear momentum -
the same underlying relationship, expressed in rotational quantities
instead of linear ones.