Moment of Inertia Calculator – AP Physics C | ShowMeClass

I

Moment of Inertia Calculator

AP Physics C · Unit 5: Rotation

Learning Objectives

Calculate I for common shapes from formulas

Apply the parallel-axis theorem: I = I_cm + Md²

Understand I = ∫r²dm as the defining integral

Compare I for different shapes at the same mass

Key Equations

Formulas Reference

Solid disk/cyl: ½MR²
Hollow cyl (ring): MR²
Solid sphere: ⅖MR²
Hollow sphere: ⅔MR²
Thin rod (center): ¹⁄₁₂ML²
Thin rod (end): ⅓ML²
Rectangular plate: ¹⁄₁₂M(a²+b²)

Moment of InertiaParallel AxisRotationAP Physics C

I_cm =—

I_axis =—

d =—

Select Shape

Mass M (kg) 2.0

Radius R (m) 0.3

Length L (m) 1.0

Width a (m) 0.5

Height b (m) 0.3

Parallel-Axis Theorem

Offset d (m) 0.0

Spin Animation

Moment of Inertia

📝 Quick Quiz▼

1. Which shape has the largest I for the same M and R?

Solid disk (½MR²) Hollow ring (MR²) Solid sphere (⅖MR²) Hollow sphere (⅔MR²)

2. The parallel-axis theorem adds _____ to I_cm:

Md Md² ½Md² M²d

3. I for a thin rod about its end is:

¹⁄₁₂ML² ⅓ML² ½ML² ML²