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The Spinner is an amusement park ride that straps people to the edge of a circle
and spins very fast. If the angular velocity of the ride is 45 revolutions per minute
and the radius of the wheel is 15 feet, find the velocity of the riders in mph.
Round your answer to the nearest tenth.

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The angular velocity is 48.38 rpm

Angular velocity is related to velocity and radius using the relation :

Velocity, V = 45 mph

Radius, r = 15 feets

w = angular velocity

w = v / r

Angular velocity in radian per minute ;

Using dimensional analysis :

1 mile = 5280 feets

1 mile = 5280 feets 1 hour = 60 minutes

1 mile = 5280 feets 1 hour = 60 minutes 1 revolution = 2π

The angular velocity is thus :

w = (45 miles/hr)×(1/15ft)×(5280ft/1mi) × (1hr/60min)×1rev/2π

w = (45×5280)/(15×60×2π)

w = 273600/5654.8667

w = 48.383 rpm

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