A bicycle wheel of radius r = 1.5 m starts from rest and rolls 100 m without slipping in 30 s. Calculate

(a) The number of revolutions the wheel makes,

(b) The number of radians through which it turns,

(c) The average angular velocity.

(a) If there is no slipping, the arc length through which a point on the rim moves equals the distance travelled. Hence, the number of revolutions is:

n = 100 m / [2π(1.5 m)] = 10.6

(b) Angular displacement:

Δθ = 2πn = s / r = 100 / 1.5 = 66.7 radians

(c) Average angular velocity:

ω̄ = Δθ / Δt = 66.7 / 30 = 2.22 rad/s