Mass Moment of Inertia

I = m k^{2} I_{cyl, axis} = \frac{1}{2} m R^{2} I = I_{G} + m d^{2}

I measures rotational inertia. Radius of gyration k is defined by I=mk². Parallel-axis: I = IG + m d² (d from the mass center). Handbook tables: slender rod, cylinder, sphere, plate.

$I$ (kg·m²): Mass moment
$k$ (m): Radius of gyration
$m$ (kg): Mass

Step-by-step solved example

Solid cylinder m=8 kg, R=0.50 m about its central axis. I?

Rotation about an axis: I = mk². Cylinder ½mR² about its centerline.

1. Table
I=½ m R²=0.5×8×0.25=1.00 kg·m².
$I = 1.00 kg \cdot m^{2}$

Answer: 1.00 kg·m²

10 practice questions

0/10 correct

1.I=mk² defines

2.Solid cylinder about its axis: I=

3.Thin hoop about its center (in-plane axis through center, perpendicular to plane): I=

4.Parallel-axis theorem adds

5.Slender rod length L about center, perpendicular: I=

6.Same rod about an end: I=

7.Sphere solid about a diameter: I=

8.Units of I_mass are

9.Larger I means, for the same α, you need

10.k for a particle at distance r from the axis is