An auto race is held on a circular track. A car completes one lap in a time of 24.6 s, with an average tangential speed of 38.0 m/s. Find (a) the average angular speed and (b) the radius of the track.

(a) 0.255 rad/s.

(b) 149.02 m

Explanation:

(a)

The expression for the average angular speed of the car is given as,

ω = 2π/T ... Equation 1

Where ω = Angular speed, T = period of the car, π = pie.

Given: T = 24.6 s,

Constant: π = 3.14

Substitute into equation 1

ω = 2 (3.14) / 24.6

ω = 0.255 rad/s.

(b)

The expression for tangential speed, angular speed and radius s given as

s = rω ... equation 2

Where s = tangential speed, r = radius of the track, ω = angular speed.

make r the subject of the equation

r = s/ω ... Equation 3

Given: s = 38 m/s, ω = 0.255 rad/s

Substitute into equation 3

r = 38/0.255

r = 149.02 m.

Hence the radius of the track = 149.02 m