Circular Motion – Period and Angular Velocity For uniform circular motion with angular velocity ω (in rad/s), the period T (time for one revolution) is:

Introduction / Context:
Period and angular velocity are reciprocally related via the constant 2π because one complete revolution corresponds to an angular displacement of 2π radians.

Given Data / Assumptions:

• Angular velocity ω in rad/s.
• Uniform circular motion (constant ω).

Concept / Approach:
Angular speed equals angle swept per unit time. One revolution is 2π radians, so time per revolution is 2π divided by the rate of angular change.

Step-by-Step Solution:
By definition: ω = dθ/dt. For one revolution: Δθ = 2π. Thus T = Δθ / ω = 2π / ω.

Verification / Alternative check:
Frequency f = 1/T, and ω = 2π f ⇒ T = 2π / ω (consistent).

Why Other Options Are Wrong:
(a) and (e) invert the relationship incorrectly. (c) multiplies instead of divides, wrong units. (d) misses a factor of 2.

Common Pitfalls:
Confusing radians with revolutions; always use 2π rad per revolution.

Final Answer:
2π / ω