Jack's bicycle tires have a diameter of 24 inches. If he rides at 15 miles per hour, what is the angular velocity of the wheels in revolutions per minute (rpm) ?

659.99 rpm

14.01 rpm

210.08 rpm

8.75 rpm

Option 3 ⇒ 210.08 rpm

Step-by-step explanation:

The relation between the angular velocity ω and the linear velocity v is v=ωr

Where r is the radius of the tire.

Given that a diameter of 24 inches. If he rides at 15 miles per hour.

∴ r = diameter/2 = 24/2 = 12 in.

And v = 15 miles/hour

Converting the speed to inches per minutes where mile = 63,360 inches and hour = 60 minuted

∴ v = 15 * 63,360/60 = 15,840 inches/minute

∴ ω = v/r = 15,840/12 = 1,320 rad/minute

Converting ω from rad per minutes to revolutions per minute

Where 1 revolution = 2π

∴ ω = 1,320 / (2π) = 210.08 rpm