Moment of Inertia of a Solid Disc
Moment of Inertia of a Solid Disc
Moment of inertia is the rotational analog of mass: it measures how much a body resists changes in its rotational speed. A solid disc — a flywheel, a wheel, a grinding wheel — is one of the most common rotating shapes in machine design, and its moment of inertia about its central axis has a simple closed form.This value feeds directly into every dynamic calculation involving the disc: the torque needed to spin it up in a given time, the kinetic energy it stores while spinning, and how it behaves when coupled to other rotating components through gears or belts.
The moment of inertia of a uniform solid disc about its central axis is I = ½mr². where m_disc is the disc mass, r_disc is the disc radius, and I_disc is the resulting moment of inertia.
Inputs
m_disc := 5 kg=5 kg
r_disc := 0.2 m=200 mm
Apply the solid-disc moment of inertia formula: because radius enters squared, a wider disc of the same mass resists spin-up far more than a narrower one.
I_disc := 0.5·m_disc·r_disc^2=0.1 kg·m^2
Results
A 5 kg, 0.2 m radius disc has a modest moment of inertia — small enough that a modest torque can spin it up quickly, which is typical for a small flywheel or pulley. Because I depends on r² but only linearly on m, redistributing the same mass toward the rim (as in a true flywheel, rather than a uniform disc) increases the moment of inertia substantially without adding weight.
Assumptions & limitations
- Uniform density throughout the disc.
- Rotation about the central axis perpendicular to the disc face.
- Rigid body (no deformation under rotation).