Question

When a body rotating along the circular path has unit linear velocity, its angular
velocity is equal to _____________ of the circular path.

Answer 1

RECIPROCAL OF RADIUS

linear speed of a body = 1 unit
time duration to cover one circle = circumference / speed
          = 2 π R / linear speed  = 2π R / 1 unit  = 2πR  units

angle it covers in one revolution = 2 π  units

so angular velocity = angle covered / time duration  =  2 π / 2 π R
       = 1/R  = 1 / Radius of circular path

Answer 2

When a body rotating along the circular path has unit linear velocity, its angular velocity is equal to radius of the circular path.