A bicyclist notes that the pedal sprocket has a radius of rp = 11 cm while the wheel sprocket has a radius of rw = 4.5 cm. The two sprockets are connected by a chain which rotates without slipping. The bicycle wheel has a radius R = 64 cm. When pedaling the cyclist notes that the pedal rotates at one revolution every t = 1.2 s. When pedaling, the wheel sprocket and the wheel move at the same angular speed. Randomized Variables rp = 11 cm rw = 4.5 cm R = 64 cm t = 1.2 s show answer Correct Answer 17% Part (a) The pedal sprocket and the wheel sprocket have the same _____________________. Tangential speed at their outer edges. ✔ Correct! show answer No Attempt 17% Part (b) Calculate the angular speed of the pedal sprocket ωp, in radians per second.

(a) The tangential speed at the outer edges of the sprocket and wheel are the same because the wheel does not slip and as a result the rotational kinetic energy delivered to/by the pedal transmitted uniformly throughout the chain and sprocket system. This energy causes the outer edges to move equal linear distances in equal time intervals.

Let s be the distance covered in time t

Let the tangential speed of the pedal sprocket be v1 and that of the wheel sprocket be v2

S = v1t = v2t since the time interval is the same and the wheel does not slip.

v1 = v2 = v

(b)The radius of the pedal sprocket r = 11cm = 0.11m

The pedal rotates 1 rev in every 1.2s. One revolution is equal to 2π radians.

So the angular speed is equal to ω = 2π/1.2s = 5.24rad/s

ω = 5.24rad/s