Rotational kinematics: choose the correct S.I. unit for angular acceleration.
Civil Engineering
SI Units
Difficulty: Easy
Choose an option
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Am/s2
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Bw/s2
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Crad/s2
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Drad/s
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Edeg/s
Answer
Correct Answer: rad/s2
Explanation
Introduction / Context:Angular acceleration quantifies how rapidly angular velocity changes with time. It appears in torque–rotation relations, rotor dynamics, and any analysis involving non-uniform circular motion. Picking the correct unit ensures that equations like tau = I * alpha remain dimensionally sound.
Given Data / Assumptions:
- Angular displacement in S.I. is measured in radians (rad), a dimensionless derived unit.
- Angular velocity has unit rad/s.
- Angular acceleration is the time derivative of angular velocity.
Concept / Approach:By definition, alpha = d(omega)/dt. If omega is in rad/s and time is in s, then alpha must be in rad/s^2. While degrees per second squared can be used informally, S.I. coherence requires radians.
Step-by-Step Solution:
Start: omega unit = rad/s.Differentiate with respect to time t (s) → alpha unit = (rad/s)/s = rad/s^2.Confirm usage in dynamics: tau = I * alpha (N·m = kg·m^2 * rad/s^2), note rad is dimensionless in S.I., preserving units.Verification / Alternative check:
Check dimensional consistency in rotational equations used in machines and mechanisms.Why Other Options Are Wrong:
m/s2: linear acceleration, not angular.w/s2: uses a letter, not a unit; undefined.rad/s: angular velocity, not acceleration.deg/s: angular velocity in degrees per second, not acceleration, and not S.I.-preferred.Common Pitfalls:
Mixing linear and angular measures.Using degrees in S.I.-based derivations leading to hidden conversion factors.Final Answer:
rad/s2