Answer to Question #262052 in Mechanics | Relativity for lowrayne

Question

Lynne jogs daily around a circular track of diameter 25 m for a total distance of

942 m in 5.0 min. (a) How many times did Lynne jog around the track? (b) What

is Lynne’s average angular speed in radians/s?

Answer 1

1) Let us calculate the length of the circular path with diameter 25 m

$L=\pi D \approx 78.54\,\mathrm{m}.$

The number of turns is

$N= \dfrac{S} {L} = \dfrac{942}{78.54} \approx 12.$

2) The average angular speed in radians per second is

$\omega =\dfrac{2\pi}{T},$ where T is time needed for jogging around one circular track.

$T =\dfrac{5\cdot 60\,\mathrm{s}}{N} = 25\,\mathrm{s}.$

Therefore, the angular velocity is

$\omega=\dfrac{2\pi}{25\,\mathrm{s}} \approx 0.25\,\mathrm{rad/s}.$