Circular motion as a frequent case of curvilinear motion

The circle itself is the source of riddles, as well as their extraordinary solutions. This figure is used as the most commonly used symbol of eternity. Often the circle is opposed to a square. The image of the wheel and the motion along the circle are inextricably linked with the circle. In this process, the great minds of mankind not only saw the implementation of the laws of mechanics, but a philosophical sense of a constant return to oneself.

In pre-Christian times, the sign of the sun-wheel was associated with the circle. Some thinkers saw in the circle the incarnation of an infinite line, and the movement of a point along a circle was an eternal process. Astrology in the circle saw the sign forming the Zodiac line. Uroboros is a snake, which bites itself by the tail, is it another symbol denoting movement along the circumference? Mathematicians and artists found hidden meaning in this geometrical figure, and physicists, studying the motion along the circumference, created a powerful theoretical platform for explaining it by the standard laws of mechanics. Practically, curvilinear motion is the most common phenomenon. The motion of the body along the circumference is a particular, ideal case of this diverse process.

Considering the curvilinear trajectory of motion, we can represent it as a collection of arcs from circles of different radii. Accordingly, like the motion along the circumference, the curvilinear motion also has an acceleration. Motion always occurs under the influence of force, with a constant change in the direction of the velocity vector. The main condition for curvilinear motion is that the velocity vector of the body and the force acting on it tend to be directed along straight lines that intersect. Unlike rectilinear motion, the vectors of force and velocity have one direction.

If we consider even the uniform motion of the body along the circumference, we can distinguish its basic properties and features. First, this is an example of a curvilinear motion with a constant modulo velocity. Secondly, do not forget that we are dealing with acceleration, which provokes a constant change of direction. This kind of acceleration was called "centripetal". According to the classical definition, with this acceleration the body moves along the circle with a speed that is constant in modulus, and this acceleration is directed along the radius of the circle towards the center.

As for the velocity vector, here we are dealing with a quantity directed along the tangent to the trajectory. In the case of circular motion between the velocity vector and the acceleration vector, the angle is ninety degrees. Measuring the speed of a body moving in a circle, use the standard value, which is the ratio of the distance traveled to time. With this approach, the distance traveled is nothing more than the length of the arc. Also, angular displacement can be used. In this case, one can take a degree measure of the angle to which the body will move for a certain period of time, but it can be expressed in radians, or with respect to the length of the arc to the radius.

Considering the constancy of the angular velocity in the circular motion of the body, it is worthwhile to take into account several more quantities that characterize this process. This frequency and period, being quantities close, the frequency is always inversely proportional to the period. In this case, the period is the time for which the body performs a full revolution, and the frequency - the number of revolutions per unit time interval.

The study of the motion of the body in a circle is of great practical importance. Designing different machines and mechanisms is impossible without conducting accurate calculations. And it is only thanks to the laws of mechanics that it is possible to perform a fairly accurate calculation of the various shafts, wheels, flywheels and other elements that modern units and mechanisms abound.