Question

A bicyclist notes that the pedal sprocket has a radius of rp = 8.5 cm while the wheel sprocket has a radius of rw = 5.5 cm. The two sprockets are connected by a chain which rotates without slipping. The bicycle wheel has a radius R = 66 cm. When pedaling the cyclist notes that the pedal rotates at one revolution every t = 1.4 s. When pedaling, the wheel sprocket and the wheel move at the same angular speed.

Answer 1

Answer:

(a). The angular speed of the pedal sprocket is 4.48 rad/s.

(b). The linear speed of the outer edge of the pedal sprocket is 0.381 m/s.

Explanation:

Given that,

Radius of pedal = 8.5 cm

Radius of wheel = 5.5 cm

Radius of bicycle wheel = 66 cm

Time = 1.4 sec

Suppose calculate the angular speed of the pedal sprocket  and linear speed of the outer edge of the pedal sprocket.

(a). We need to calculate the angular speed of the pedal sprocket

Using formula of angular speed

$\omega_{p}=\dfrac{2\pi}{T}$

$\omega_{p}=\dfrac{2\pi}{1.4}$

$\omega_{p}=4.48\ rad/s}$

(b). We need to calculate the linear speed of the outer edge of the pedal sprocket

Using formula of linear speed

$v_{p}=r_{p}\times\omega_{p}$

Put the value into the formula

$v_{p}=8.5\times10^{-2}\times4.48$

$v_{p}=0.381\ m/s$

Hence, (a). The angular speed of the pedal sprocket is 4.48 rad/s.

(b). The linear speed of the outer edge of the pedal sprocket is 0.381 m/s.