Angular Velocity – Valid Units in Engineering Practice Which of the following are valid units for angular velocity (rate of rotation)?

Introduction / Context:
Angular velocity measures how fast an object rotates about an axis. In mechanical design (shafts, gears, flywheels), expressing angular speed in the correct units is essential for power and kinematics calculations.

Given Data / Assumptions:

• Angular displacement is measured in radians (SI) or revolutions (engineering usage).
• Time is measured in seconds or minutes.

Concept / Approach:
Angular velocity ω is change of angular position per unit time. The SI coherent unit is rad/s. In practice, rotating machinery often uses rpm (rev/min). Both are acceptable, with conversion 1 rev = 2π rad, so 1 rpm = 2π/60 rad/s.

Step-by-Step Solution:
Definition: ω = Δθ / Δt. SI unit: rad/s (radian is dimensionless but treated as a unit of angle). Common industry unit: rev/min (rpm). Therefore, both rad/s and rev/min are valid units of angular velocity.

Verification / Alternative check:
For a motor rated 1500 rpm: ω = 1500 * 2π/60 ≈ 157.08 rad/s. The conversion shows consistency between the two units.

Why Other Options Are Wrong:
m/min: linear speed, not angular. N·m/s: power unit (watt) equivalence, not angular speed.

Common Pitfalls:
Confusing linear speed v with angular speed ω; they relate by v = ω r. Mixing rpm and rad/s without proper conversion.

Final Answer:
both rad/s and rev/min