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95/3334–6FE Reference Handbook 10.4 · Dynamics · Rigid-body kinetics
1. Constant Acceleration2. Newton’s Second Law3. Work–Energy Principle4. No-Time Acceleration Equation5. Position–Time Equation6. Impulse–Momentum Principle7. Translational Kinetic Energy8. Normal (Centripetal) Acceleration9. Level-Ground Projectile Range10. Power11. Angular Form of Newton’s Second Law12. Relative Velocity13. Coefficient of Restitution14. Elastic Spring Energy15. Rigid-Body Rotation: Tangential and Normal Accel.16. Mass Moment of Inertia17. Conservation of Mechanical Energy18. Angular Impulse–Momentum19. Rolling Without Slip20. Polar / Path Normal–Tangential Acceleration21. Instantaneous Center of Zero Velocity22. Work of a Variable Force

Handbook formula

Angular Form of Newton’s Second Law

The resultant moment about the mass center (or a fixed axis) equals the mass moment of inertia times angular acceleration. I is larger when mass lies farther from the axis. For a particle, I = m r².

(N·m)
Resultant moment
(kg·m²)
Mass moment of inertia
(rad/s²)
Angular acceleration

Step-by-step solved example

A rotor has I = 4.0 kg·m². What moment produces α = 3.0 rad/s²?

TL
ΣM = Iα about the shaft axis.

  1. 1. Apply ΣM = Iα

    ΣM = 4.0 × 3.0 = 12.0 N·m.

  2. 2. Direction

    Moment and α share the same sense about the axis.

Answer: 12.0 N·m

10 practice questions

0/10 correct

1.I = 2 kg·m², α = 5 rad/s². ΣM =

2.If ΣM = 0, then α is

3.I of a particle about an axis is

4.Solid circular cylinder (or disk) about its central axis: I ≈

5.Disk I = 0.50 kg·m², M = 4.0 N·m. α =

6.The rotational analog of F = ma is

7.SI units of I are

8.α = 0 while the body is spinning means

9.I = 10 kg·m², α = 0.40 rad/s². ΣM =

10.Moving mass farther from the axis