# How fast is a point at the top of the tire moving?

A typical road bike wheel has a diameter of 70 cm including the tire.

A) In a time trial, when a cyclist is racing along at 12 m/s how fast is a point at the top of the tire moving?

B) How fast, in rpm, are the wheels spinning?

• Part A. The velocity for a point on the top of a tire would be 2V (2*12m/s)=24m/s

Part B. is just converting 12m/s into rad/s. Angular velocity = V/r ((12m/s)/0.35m)=34.2857 rad/s. Now convert into revolutions by dividing by 2pi to get revs per second, and multiply by 60 seconds to get 327.4 rpm.

• hey mastering physics gamers, the correct answers are

A) 24 m/s

B) 330 rpm

• A) The point at the top of he tire will also cover 12 m/s in a circular route.

B) rpm of wheels = angular velocity in rad/s x (1 revolutions / 2π) in rev/s x (60 s / 1 min)

rpm of wheels = (v/r) x (1/2π) x (60)

rpm of wheels = (12 m/s)/(0.35 m) x (1/2π) x (60) = 327.4 rpm

• A) In a time trial, when a cyclist is racing along at 12 m/s how fast (Vt) is a point at the top of the tire moving?

Vt= 12 m/sec

B) How fast, in rpm, are the wheels spinning?

ω = Vt/r = 12/0.35 rad/sec = 2*PI*n/60

n = 12*60/(0.7*PI) = 1028.57/PI rpm ( ≅ 327.40 )

• 12 m/s and 327.4 Rpm