Question

A racing car travels on a circular track of radius 158 m, moving with a constant linear speed of 19.1 m/s. Find its angular speed. Answer in units of rad/s.

Answer 1

`\omega=0.12(rad)/(s)`

Step-by-step explanation:

In a uniform circular motion, since a complete revolution represents 2π radians, the angular velocity, which is defined as the angle rotated by a unit of time, is given by:

`\omega=(2\pi)/(T)(1)`

Here T is the period, that is, the time taken to complete onee revolution:

`T=(2\pi r)/(v)(2)`

Replacing (2) in (1):

`\omega=(2\pi)/((2\pi r)/(v))=(v)/(r)\\\omega=(19.1(m)/(s))/(158m)\\\omega=0.12(rad)/(s)`