Question Detail
Question
For a particle in uniform circular motion of radius r with constant angular speed ω, the magnitude of its angular momentum about the center is given by which expression?
Correct Answer
Option B is the correct answer.
Detailed Explanation
For a particle in circular motion, the position vector r (from the center) and the linear momentum p (tangential) are perpendicular. Thus, the magnitude of angular momentum L = r p sin 90° = r p = r (m v). Since v = ω r for circular motion, substituting gives L = r m (ω r) = m r² ω.
Hint
Start with the definition L = r p for the perpendicular case, then relate the linear speed v to angular speed ω.