Units of angular acceleration (single correct): Which of the following is a correct unit for angular acceleration in mechanics? Choose the best answer.

Introduction / Context:
Angular acceleration quantifies the time rate of change of angular velocity. Correctly identifying its units is fundamental in dynamics, rotational kinematics, and control of rotating machinery, where dimensional consistency ensures correct formulation of equations of motion.

Given Data / Assumptions:

• Angular velocity has units of angle per time (e.g., rad/s).
• Angular acceleration is the derivative of angular velocity with respect to time.
• Any angle unit can be used, but the SI coherent unit is the radian.

Concept / Approach:
If ω is in rad/s, then α = dω/dt has units (rad/s)/s = rad/s^2. Degree-based units like deg/s^2 can be used in non-coherent contexts, but must be converted to radians for SI equations (1 rad ≈ 57.2958°). Linear acceleration m/s^2 applies to translational motion, not angular quantities.

Step-by-Step Solution:

Verification / Alternative check:
Dimensional analysis: angles are dimensionless in SI but carried symbolically; time has dimension T. Therefore α has dimension T^−2, matching rad/s^2.

Why Other Options Are Wrong:

• deg/s: angular velocity unit, not acceleration.
• rev/s: angular velocity unit.
• m/s^2: linear acceleration, not angular.
• N/m: stiffness unit, unrelated to acceleration.

Common Pitfalls:
Mixing angular and linear measures; forgetting the “per second squared”.

Final Answer:
radians per second squared (rad/s^2)