An auto race is held on a circular track. A car completes one lap in a time of 1

Question

An auto race is held on a circular track. A car completes one lap in a time of 17 s, with an average tangential speed of 66 m/s. Find (a) the average angular speed and (b) the radius of the track. The take-up reel of a cassette tape has an average radius of 1.20 cm. Find the length of tape that passes around the reel in 32 s when the reel rotates at an average angular speed of 2.4 rad/s. Suppose you are riding a stationary exercise bicycle, and the electronic meter indicates that the wheel is rotating at 18 rad/s. The wheel has a radius of 0.90 ft. If you ride the bike for 32 min, how far would you have gone if the bike could move?

Explanation / Answer

here,

5)

the time taken , t = 17 s

average tangential speed , v = 66 m/s

a)

the average angular speed , w = 2 * pi /T

w = 2 * pi /17 = 0.37 rad/s

b)

the radius of the track , r = v /w

r = 66/0.37 = 178.7 m

the radius of the track is 178.7 m

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