Question

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

Answer 1

Answer:

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