A bicycle with a 26-inch diameter wheel is traveling at 20 miles per hour. Find the angular speed of the wheels, in radians per minute, rounding to the nearest whole number.

Answer 1

I mile = 5280 feet = 5280 x 12 = 63360 inches.

1 hour = 60 minutes.

So inches per minute that a point on the circumference moves = ( 63360 x 20) / 60 = 21120

The radius of the wheel is 26 /2 = 13 inches

So circumference = 2πr = 26π

So the wheel will turn through 21120 / 26π circumferences in a minute

1 circumference is 2π radians, so 21120 / 26π x 2π = (21120 x 2) / 26 radians per minute