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ASME SI-3-1975 — SI Units in Dynamics (First Edition)
🏃 ASME SI-3-1975 is the third booklet in the ASME International System (SI) of Units series, dedicated to SI units in dynamics, first published in December 1975 (second printing, February 1978). The booklet supports students, teachers, and engineers in practice, helping them apply the SI unit system correctly within the branch of mechanics that studies the relation between forces and the motion of bodies.
💡 Following the series philosophy, a problem whose input is given in SI terms should be solved in SI — no mid-stream conversion back to U.S. Customary units. A consistent SI set for force, mass, and acceleration eliminates the conversion confusion inherent in gravitational engineering units.
1. Overview and Scope 📌
Dynamics is that part of mechanics which deals with the relation between forces and the motion of bodies. When the mass of a body may be considered to be localized at a point, the study is known as particle dynamics; more generally, when the geometry of the body is significant, we deal with extended body dynamics, and extended bodies may be rigid or nonrigid. An important property of an extended body that enters the force-motion relation is the moment of inertia, a central parameter of rigid-body dynamics.
The booklet is organized as follows: Section 1, Introduction; Section 2, Units and Conversion Factors; Section 3, Solved Problems; Section 4, Practice Problems with Answers. The tables list the principal quantities encountered in dynamics and their units, derived units, and commonly used conversion factors.
⚠️ Note that the booklet is not a dynamics textbook: it assumes the reader is familiar with the principles of the subject and focuses on the transition from U.S. Customary units to SI units, so use it alongside a formal dynamics course.
2. Principal Quantities and Unit Systems 🔧
The principal quantities encountered in dynamics, in both U.S. Customary and SI (metric) units, are tabulated below:
| Quantity | U.S. Customary Unit (Symbol) | SI Unit (Symbol) |
|---|---|---|
| Linear acceleration | ft/s² | m/s² |
| Angular acceleration | rad/s² | rad/s² |
| Force | lbf | newton (N) |
| Mass | slug (lbf·s²/ft) | kilogram (kg) |
| Energy / work | ft·lbf | joule (J) |
| Power | horsepower (hp) | watt (W) |
| Linear momentum / impulse | lbf·s | N·s |
| Angular momentum / angular impulse | lbf·ft·s | N·s·m |
| Mass moment of inertia | slug·ft² | kg·m² |
| Radius of gyration | ft | m |
| Torque | lbf·ft | N·m |
| Rotational frequency | rev/s, rad/s | s⁻¹, rad/s |
| Plane angle | degree (°) | radian (rad) |
In SI, Newton’s second law F = ma requires no conversion constant: 1 N = 1 kg·m/s². In the rotational relation M = I·α, substituting I in kg·m² and α in rad/s² yields the torque directly in N·m — the units are self-consistent by construction.
🚨 In U.S. engineering units the coexistence of lbf and lbm forces the introduction of the conversion constant gc = 32.174 lbm·ft/(lbf·s²) in Newton’s law. The SI system eliminates that nuisance entirely; treating “pound force” as “pound mass” in F = ma will inevitably produce unit errors.
3. Commonly Used Conversion Factors ⚖️
| Quantity | Conversion | Factor |
|---|---|---|
| Force | lbf to N | 4.448222 |
| Mass | slug to kg | 1.459390 × 10¹ |
| Linear momentum / impulse | lbf·s to N·s | 4.448222 |
| Mass moment of inertia | slug·ft² to kg·m² | 1.355818 |
| Angular momentum | lbf·ft·s to N·s·m | 1.355818 |
| Energy / work | ft·lbf to J | 1.355818 |
| Power | hp (550 ft·lbf/s) to W | 7.456999 × 10² |
| Length | ft to m | 3.048 × 10⁻¹ |
| Length | in to mm | 2.54 × 10¹ |
| Plane angle | degree to rad | 1.745329 × 10⁻² |
| Rotational frequency | rev/min to rad/s | 1.047198 × 10⁻¹ |
| Stress / pressure | lbf/in² to Pa | 6.894757 × 10³ |
For example, 1 slug = 1.459390 × 10¹ kg ≈ 14.594 kg; 1 rev/min = 2π/60 rad/s ≈ 0.10472 rad/s; and 1 slug·ft² = 1.355818 kg·m², useful for flywheel and rotor dynamics.
💡 Useful SI magnitudes: a passenger car weighs about 1–2 tonnes (1000–2000 kg); rotating machinery moments of inertia commonly range from 0.1 to 100 kg·m²; torques of several N·m correspond to domestic motors, while kN·m torques belong to large turbines and rolling mills.
4. Worked Examples and the SI Approach ✏️
The solved problems cover the principal problem types of dynamics, and their SI forms make the magnitudes immediately intuitive:
- Newton’s second law: solve F = ma directly — e.g., a 1200 kg car accelerating at 2 m/s² requires a traction force F = 2400 N = 2.4 kN.
- Work-energy: kinetic energy T = ½mv² and potential energy V = mgh are both expressed in joules, so the energy-conservation equation is automatically consistent.
- Momentum and impulse: impulse Ft = Δ(mv) with F in N, t in s, and mv in kg·m/s (= N·s).
- Rigid-body rotation: M = I·α with the mass moment of inertia in kg·m².
⚠️ The numerical value of momentum in kg·m/s equals that of impulse in N·s, but always write the defining relation and keep track of signs along the direction of time in collision and impact problems.
5. Engineering Practice Essentials 🛠️
- 🔍 Multibody dynamics simulation: adopt a consistent base set of kg, m, N, and rad in analysis software; do not mix unit systems at inputs or outputs.
- 🔧 Rotor balancing and flywheel design: compute mass moments of inertia and radii of gyration in kg·m² and m, matching SI-based rotor drawings and structural shape data.
- 📊 Impact and shock absorption: use N·s for impulse and momentum exchange and pair it with the energy-absorption capacity (J) of buffers and dampers.
- 📋 Teaching practice: rewrite U.S. Customary exercises (lb/ft/slug) into kg/m/N and re-solve them until the magnitudes feel natural.
✅ Verification routine: after solving, first check units by dimensional analysis (a force must come out as kg·m/s² = N), then check magnitudes against intuition (a person weighs about 600–900 N; a family car needs about 2–5 kN of traction force).
6. Frequently Asked Questions ❓
❓ Q: Why is no gc conversion constant needed in SI?
A: Because SI defines the newton as kg·m/s², so F = ma is exactly self-consistent (1 N = 1 kg × 1 m/s²). The gravitational engineering system that keeps both lbf and lbm requires gc ≈ 32.174 lbm·ft/(lbf·s²) to be applied in the same equation.
A: Because SI defines the newton as kg·m/s², so F = ma is exactly self-consistent (1 N = 1 kg × 1 m/s²). The gravitational engineering system that keeps both lbf and lbm requires gc ≈ 32.174 lbm·ft/(lbf·s²) to be applied in the same equation.
❓ Q: Why is the (mass) moment of inertia in kg·m² rather than kg·m⁴?
A: Two different “moments of inertia” exist: the mass moment of inertia I = Σmr² in dynamics, with unit kg·m², and the area moment of inertia (second moment of area) in strength of materials, with unit m⁴. This booklet deals with the former.
A: Two different “moments of inertia” exist: the mass moment of inertia I = Σmr² in dynamics, with unit kg·m², and the area moment of inertia (second moment of area) in strength of materials, with unit m⁴. This booklet deals with the former.
❓ Q: Should angular velocity be written rad/s or s⁻¹?
A: The radian is dimensionless, but writing rad/s explicitly distinguishes angular velocity from ordinary frequency (Hz or s⁻¹). In dynamics practice, write rad/s; when rotational speed is given in r/min or r/s, convert to rad/s first.
A: The radian is dimensionless, but writing rad/s explicitly distinguishes angular velocity from ordinary frequency (Hz or s⁻¹). In dynamics practice, write rad/s; when rotational speed is given in r/min or r/s, convert to rad/s first.
🔍 Q: How does this booklet sit within the SI series?
A: Start with SI-1 (the orientation guide), then use the discipline booklets as needed — SI-2 (strength of materials), SI-3 (dynamics), SI-4 (thermodynamics), SI-5 (fluid mechanics), SI-6 (kinematics), SI-7 (heat transfer), SI-8 (vibration), SI-9 (energy conversion), SI-10 (steam charts). Dynamics (SI-3) and kinematics (SI-6) are frequently consulted together: one explains why bodies move, the other how they move.
A: Start with SI-1 (the orientation guide), then use the discipline booklets as needed — SI-2 (strength of materials), SI-3 (dynamics), SI-4 (thermodynamics), SI-5 (fluid mechanics), SI-6 (kinematics), SI-7 (heat transfer), SI-8 (vibration), SI-9 (energy conversion), SI-10 (steam charts). Dynamics (SI-3) and kinematics (SI-6) are frequently consulted together: one explains why bodies move, the other how they move.
