What is the angular velocity of an object in a horizontal circular path of radius 1.5m with a constant speed of 12$ms^{-1}$?

Analyze the question You are given the radius r = 1.5 m and the linear speed v = 12 m/s, and you need the angular velocity ω.

Concept Linear speed and angular velocity are related by:

v = ωr, so ω = v / r

Solution ω = 12 / 1.5 = 8 rad/s

Answer The calculation gives 8.0 rad/s, which is option C.

Tip When a question gives speed and radius and asks for angular velocity, just divide: ω = v/r. Remember the related formulas too:

• a = v²/r = ω²r (centripetal acceleration)
• ω = 2πf = 2π/T

Check your units: m/s ÷ m = s⁻¹, which is rad/s.