How Do You Calculate Angular Velocity for a Bicycle Tire?

[Imperil]

A bicycle travels at 18 km/h. The tires on the bicycle are 70 cm in diameter. Determine the angular velocity in rad/s.

My work:

18 km/h = 1800000 cm / 60^2 s = 500 cm / s
C = 2Pi(35 cm) = 70Pi cm
500 cm / 70Pi cm = 2.3 rotations / s
2.3 x 2Pi = 4.6Pi rad/sec

First I determine the speed in cm / s, then the circumference of the tire, divide the speed by circumference to get number of rotations per second, then multiply the number of rotations by 2PI which then gives me 4.6PI rad/sec

Am I correct? Or have I done something wrong?

 

[HallsofIvy]

I didn't check your arithmetic but your reasoning is correct.

 

[Architeuthis Dux]

Your solution is correct. You correctly converted the speed from km/h to cm/s and then used the formula for angular velocity (ω = v/r) to determine the number of rotations per second. Multiplying by 2π gives the angular velocity in radians per second. Well done!