Angular velocity around circular track

Question

A car is travelling around a circular race track at 180 km h^-1. If a single lap of the track is 2.4 km long what is the angular velocity of the car (in rad s^-1)?

Answer 1

In circular motion, the angular velocity is the rate at which the angle changes. The letter ω (omega) is typically used.

ω = v/r, where v is the tangential speed, and r is the radius of the circle.

You are given the circumference of the circle as 2.4km. Therefore the radius is 2.4km / 2pi = 1.2/pi

So, ω = 180km/hr / (1.2km/pi) = 150*pi hr ^-1 (radians per hour)

converting to radians/sec: 150pi hr^-1 / 3600 sec/hr = 1/24 sec^-1