Rotational Inertia & Acceleration Torque
Rotor dynamics & motor starting analysis
Rotor Geometry Selection
Acceleration Torque Calculation
Angular Acceleration Required
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Acceleration Torque (I × α)
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Net Torque Required
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Acceleration Margin
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Notes: Net torque = Acceleration torque + Load torque. Pull-up must exceed net torque. Margin = (Pull-up − Net) / Load × 100%. Design target: 15–25% margin.
Moment of Inertia & Acceleration Formulas
Solid Cylinder / Disk (axis perpendicular)
I = (1/2) × M × R²
Motor rotors, impellers, flywheels, brake drums
Hollow Cylinder / Ring
I = (1/2) × M × (R_o² + R_i²)
Hollow shafts, sleeves, thin-walled structures
Solid Sphere
I = (2/5) × M × R²
Spherical rotors, ball elements
Thin Spherical Shell
I = (2/3) × M × R²
Hollow spheres, thin-walled rotating pressure vessels
Rod (about center, perpendicular)
I = (1/12) × M × L²
Rotating shafts, connecting rods
Angular Acceleration
α = ω_f / t_acc
ω_f = final angular speed (rad/s), t = time (s)
Acceleration Torque from Inertia
T_acc = I × α
Torque required to accelerate the rotor and load
Net Torque Balance
T_net = T_acc + T_load
Total motor torque demand during acceleration
Acceleration Margin
Margin (%) = (T_pullup − T_net) / T_load × 100
Available margin beyond load. Typical minimum: 15–25%