Question

The wheel has a radius of 35 cm while the rear sprocket has a radius of 3.5 cm. Assume that the wheel drives both sprocket and axle. If the axle has a radius of 1 cm, determine:

(i) the velocity ratio of the sprocket and axle.

(ii) the velocity ratio of the wheel and sprocket.

(iii) The velocity ratio of wheel and axle

Answer 1

To determine the velocity ratio of the sprocket and axle, we first need to calculate the circumferences of the sprocket and the axle:

Circumference of sprocket = 2π * radius = 2π * 3.5 cm = 7π cm
Circumference of axle = 2π * radius = 2π * 1 cm = 2π cm

(i) Velocity ratio of sprocket and axle:
Velocity ratio = Circumference of sprocket / Circumference of axle
Velocity ratio = 7π cm / 2π cm = 3.5

So, the velocity ratio of the sprocket and axle is 3.5.

To determine the velocity ratio of the wheel and sprocket, we can use the same formula:

(ii) Velocity ratio of wheel and sprocket:
Velocity ratio = Circumference of wheel / Circumference of sprocket
Velocity ratio = 2π * 35 cm / 7π cm = 10

So, the velocity ratio of the wheel and sprocket is 10.

To determine the velocity ratio of the wheel and axle, we can calculate the circumferences of the wheel and axle:

Circumference of wheel = 2π * radius = 2π * 35 cm = 70π cm

(iii) Velocity ratio of wheel and axle:
Velocity ratio = Circumference of wheel / Circumference of axle
Velocity ratio = 70π cm / 2π cm = 35

So, the velocity ratio of the wheel and axle is 35.