Uniform circular motion — if a particle moves on a circle of radius r with constant angular velocity ω (rad/s), the maximum centripetal acceleration equals ω²r. Is this statement correct?

Introduction / Context: In kinematics, a body moving along a circular path with constant angular velocity experiences centripetal acceleration directed toward the center. Understanding its magnitude is a core skill for dynamics and machine theory.

Given Data / Assumptions:

• Radius of circular path = r.
• Angular velocity = ω (constant).
• Uniform circular motion; tangential acceleration is zero.

Concept / Approach: Centripetal (normal) acceleration for circular motion is a_n=v²/r. With v=ωr, we get a_n=(ωr)²/r=ω²r. Its direction is radial inward. Since magnitude is constant for uniform motion, the maximum equals this constant value ω²r.

Step-by-Step Solution:

Verification / Alternative check: Using curvature κ=1/r and speed v, the normal acceleration is v²κ=ω²r; both formulations agree.

Why Other Options Are Wrong:
Wrong — would contradict the standard relation a_n=ω²r for uniform circular motion.

Common Pitfalls: Confusing centripetal and tangential acceleration; assuming acceleration is zero because speed is constant—direction changes, so acceleration exists.

Final Answer: Right.