An object moves in a circular path of radius 0.5m with a speed of 1$ms^{-1}$ What is its angular velocity?

Analyze the question: An object moves in a circle of radius r = 0.5 m at a linear speed v = 1 m/s. We need its angular velocity, ω.

Concept: Linear speed and angular velocity are related by:

v = ωr, so ω = v / r

Solution:

ω = v / r = 1 / 0.5 = 2 rad/s

Check with the options:

• A. 8 rad/s: too large
• B. 4 rad/s: too large
• C. 2 rad/s: matches
• D. 1 rad/s: this is just the speed value, which would only be right if r = 1 m

Tip: Students often mix up the formulas. A quick way to remember is that ω is "per radius," so the angular velocity is always the linear speed divided by r. You can also check the units: m/s ÷ m = 1/s, which is rad/s. If the radius is less than 1 m, ω will always be bigger than v numerically.