Components of acceleration in circular motion\nWhen a particle moves along a circular path, does its acceleration have both normal (centripetal) and tangential components?

Introduction / Context:
Nonlinear motion is analyzed by decomposing acceleration into components aligned with the path (tangential) and toward the center of curvature (normal or centripetal). Understanding this decomposition is vital in dynamics.

Given Data / Assumptions:

• Particle follows a circular trajectory of radius r.
• Speed may be constant or varying with time.

Concept / Approach:
Acceleration a is resolved as a = a_t + a_n, where a_t = dv/dt (along the direction of motion) and a_n = v^2 / r (directed toward the center). For circular motion, a_n exists whenever v ≠ 0. If speed varies, a_t is nonzero; if speed is constant, a_t = 0 but a_n remains.

Step-by-Step Solution:

Verification / Alternative check:
Uniform circular motion: dv/dt = 0 ⇒ a_t = 0; still a_n = v^2 / r. Nonuniform: both a_t and a_n nonzero, confirming the general statement.

Why Other Options Are Wrong:

• “False” would deny the normal component which is fundamental to circular motion for v ≠ 0.

Common Pitfalls:
Equating acceleration solely with change in speed; change in direction also constitutes acceleration via the normal component.

Final Answer:
True