# Circular motion transmission

It is common to see people riding a bicycle, whether at leisure or going to work. At other times, we also see mechanics checking the engine part of the cars in order to verify their condition. In both cases we see physics embedded, although many people don’t even know it. In the examples discussed above, we have the transmission of circular motion through the belt, for the cars; and chain, in the example of bicycles.

We can also find this type of transmission in industries, which always use a single motor in order to start several machines. In the figure above we have a basic example of circular motion transmission, in which we can see that wheel **A** is composed of two concentric pulleys, which turn two other pulleys. Let’s imagine that wheel A is connected to the axle of a motor, rotating with constant speed, and that it sets in motion, by means of belts, wheels **B** and **C** .

First, let’s analyze the movements of points 1 and 2, which belong to wheel **A. **The two points have the following characteristics:

*– equal frequencies, that is, f _{1} = f _{2} ;
– equal periods, T _{1} = T _{2} ;
– equal angular velocities, ω _{1} = ω _{2} ;
– different scalar speeds – because the greater the radius of the circumference, the greater the scalar displacement performed in the same time. Thus, v _{1} > v _{2} .*

*– equal scalar speeds, as points 1 and 3 are points in contact with the belt and have constant speed, that is, v _{1} = v _{2} ;
– different angular speeds, as the smaller wheel must rotate faster to follow the larger wheel, therefore, ω _{3} > ω _{1} ;
– different frequencies, ie f _{3} > f _{1} ;
– different period, T _{3} < T _{1} .*

Considering that the speeds of points 1 and 3 are the same, we can show that the frequencies are inversely proportional to the radii of the wheels: