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

Answer 1

Hello Shelby,

Note that the problem has two different length units: inches and miles, and two different time units: hours and minutes. So you need to pick one of each type of unit in solving the problem. For example, you might use inches and minutes. If you do that, figure out how many inches per minute is the same as 26 miles per hour. That will be how far the bicycle goes in one minute. Then you need to find out how many turns of the wheel it takes to go this number of inches. One turn of the wheel would be the circumference of the wheel (inches). Once you have the number of turns per minute, each turn will be 2 pi radians so you can convert it to radians per minute. Each conversion step requires multiplying or dividing by some number (such as 5280 for changing miles to inches). Tom S.

Answer 2

At 20 mph the bike is traveling 20 miles / hr x 5280 ft / mile / 60 min / hr. 1= 1760 ft / min.

As the diameter of the wheel is 26 inches, the circumference is pi x 26 inches / 12 inches / ft = 6.81 ft.

Therefore in one minute the wheel undergoes 1760 ft/min x 1 rev / 6.51 ft = 270.4 rev / min.

As one revolution is 2 x pi radians, the angular speed of the wheels is 2 x pi rad / rev x 270.4 rev / min = 1698 rad / min. or 1700 rad / min to two sig figs.