What is centripetal acceleration?

Imagine a point on the coordinate plane. Two rays emanating from it form an angle. Its value can be determined in both radians and degrees. Now, at some distance from the point-center, we will mentally draw a circle. The measure of the angle expressed in radians in this case is the mathematical ratio of the arc length L separated by two rays to the distance between the center point and the circle line (R), that is:

Fi = L / R

If we now present the described system as material, then not only the concept of angle and radius can be applied to it, but also centripetal acceleration, rotation, etc. Most of them describe the behavior of a point located on a rotating circle. By the way, a solid disk can also be represented by a set of circles, the difference of which is only in the distance from the center.

One of the characteristics of such a rotating system is the period of circulation. It indicates the value of the time at which the point on an arbitrary circle returns to the initial position or, which is also true, will turn 360 degrees. At a constant rotation speed, the correspondence T = (2 * 3.1416) / Ug (here and later Ug - angle) is satisfied.

The frequency of rotation indicates the number of full revolutions performed in 1 second. At a constant speed, we get v = 1 / T.

The angular velocity depends on the time and the so-called angle of rotation. That is, if we take as an origin the arbitrary point A on the circle, then during the rotation of the system this point will shift to A1 in time t, forming an angle between the radii of the A-center and the A1-center. Knowing the time and angle, you can calculate the angular velocity.

And if there is a circle, movement and speed, then there is also a centripetal acceleration. It is one of the components that describe the movement of a material point in the case of curvilinear motion. The terms "normal" and "centripetal acceleration" are identical. The difference is that the second one is used to describe the motion along the circle, when the acceleration vector is directed to the center of the system. Therefore, it is always necessary to know exactly how the body (point) moves and its centripetal acceleration. Its definition is as follows: it is the rate of change of velocity, whose vector is directed perpendicular to the direction of the instantaneous velocity vector and changes the direction of the latter. The encyclopedia states that Huygens was studying this question. The formula for the centripetal acceleration proposed by him looks like:

Acs = (v * v) / r,

Where r is the radius of curvature of the traversed path; V - speed of movement.

The formula by which centripetal acceleration is calculated still causes heated controversy among enthusiasts. For example, a curious theory was recently announced.

Huygens, considering the system, proceeded from the assumption that the body moves along a circle of radius R with a velocity v measured at the initial point A. Since the vector of inertia is directed along the tangent to the circle, we obtain a trajectory in the form of a straight line AB. However, the centripetal force keeps the body on a circle at the point C. If we denote the center by 0 and draw the lines AB, BO (the sum of BS and CO), and also AO, we get a triangle. In accordance with the law of Pythagoras:

OA = CO;

AB = t * v;

BS = (a * (t * t)) / 2, where a is the acceleration; T is time (a * t * t - this is speed).

If we now use the formula of Pythagoras, then:

R2 + t2 + v2 = R2 + (a * t2 * 2 * R) / 2+ (a * t2 / 2) 2, where R is the radius, and alphanumeric writing without the sign of multiplication is a power.

Huygens admitted that, since the time t is small, it can be ignored in the calculations. Having transformed the previous formula, it came to the well-known Acs = (v * v) / r.

However, since time is taken in the square, a progression occurs: the greater t, the higher the error. For example, for 0.9, an almost final value of 20% is not taken into account.

The concept of centripetal acceleration is important for modern science, but, obviously, it is too early to put an end to this question.