Question

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.

Answer 1

Answer:

(a) See explanation below.

(b) ω = 5.24rad/s.

Explanation:

(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