Period and frequency in uniform circular motion

Communication satellites are placed in orbit so that they rotate around the Earth each day.

It is notable that in our daily lives it is easy to verify objects and bodies that describe a circular movement, for example, the wheel of a bicycle, the movement of a weather vane, motor pulleys, etc. With this, we can say that circular motion is one of the most important studies, since the vast majority of machines we use are based on this type of motion.

Period and frequency

Let’s see the figure above in which we have a disk that constantly rotates on its own axis. It is possible to measure the time taken by the disk to complete one revolution about its axis, that is, to complete one revolution. The time it takes the disk to make one complete revolution is called the period or period of revolution and to represent the period we will use the letter T .

In the International System of Units ( SI ), the period of revolution is measured in seconds, so that means to say that the period is the number of seconds per revolution. Therefore, we can define that the disk in the figure above makes a complete revolution in exactly T seconds.

As we mentioned earlier that the disk rotates constantly, we can define another quantity, the frequency. In physics, the number of turns the disk makes per unit of time is called its frequency .

We define the frequency as being the inverse of the period, that is, in the International System of Units (SI), the frequency is nothing more than the number of revolutions given each second. For example, if a disk makes 10 revolutions per second, we say that each revolution is 1/10th of a second.

In (SI), the unit of measurement for frequency is 1/s, or s -1 , or even hertz, represented by Hz. A frequency of 20 Hz indicates that the object rotates at a rate of 20 revolutions per second. The frequency is indicated by the letter f .

Mathematically, we have that the period and frequency are given, respectively, by:

Note: When circular motion has constant period and frequency, it is considered uniform circular motion (MCU).

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