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Mechanics
Mechanics

Moment of Inertia (Solid Sphere)

I=25MR2I = \frac{2}{5}MR^2

Moment of inertia of a uniform solid sphere rotating about any diameter.

Variables

I
Moment of inertia
Rotational inertia
kg·m²
M
Mass
Total mass of sphere
kg
R
Radius
Radius of sphere
m

Derivation

I = ∫r²dm. Using spherical coordinates and integrating over the volume gives I = (2/5)MR².

Your notes

0/5000

Common questions

What is the Moment of Inertia (Solid Sphere) formula?

Moment of Inertia (Solid Sphere) is written I = 2/5MR². Moment of inertia of a uniform solid sphere rotating about any diameter. It belongs to Mechanics, under Rotational Motion.

What are the units in I = 2/5MR²?

In SI units, I is moment of inertia, measured in kg·m²; M is mass, measured in kg; R is radius, measured in m.

How is the Moment of Inertia (Solid Sphere) formula derived?

I = ∫r²dm. Using spherical coordinates and integrating over the volume gives I = (2/5)MR². The result is I = 2/5MR².