Imagine a point on the coordinate plane.Two rays emanating from it, form an angle.Its value can be defined as in radians or degrees.Now at some distance from the center point to mentally draw a circle.The measure of the angle, expressed in radians, in such a case is a mathematical ratio of arc length L, is separated in two beams, the value of the distance between the center point and the line of a circle (R), ie:
Fi = L / R
If we now imaginedescribed system material, then it can be applied not only to the concept of angle and radius, but also centripetal acceleration, rotation, etc.Most of them describe the behavior of a point on a rotating circumference.Incidentally, a solid disk can also be represented by a set of circles which only the difference in distance from the center.
One of the characteristics of such a rotating system - a period of revolution.He points to the importance of time for which an arbitrary point on the circle back to the starting position and that is also true, will turn 360 degrees.At constant speed runs matching T = (2 * 3.1416) / Ug (hereinafter Ug - angle).
Speed indicates the number of full revolutions performed in 1 second.At a constant speed of v = 1, we obtain / T.
angular velocity depends on time, and so-called angle of rotation.That is, if we take the origin of an arbitrary point A on the circle, then the rotation of the shift to the A1 point in time t, forming an angle between the radii of the A-center and the A1 facility.Knowing the time and angle, one can calculate the angular velocity.
And time is a circle, movement and speed, so 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 is used to describe a circular movement when the acceleration vector is directed towards the center of the system.Therefore it is always necessary to know exactly how to move the body (point) and the centripetal acceleration.Defining it as follows: it is the rate of change of velocity vector is directed perpendicular to the direction of the instantaneous velocity vector and changes the orientation of the latter.The encyclopedia states that the study of the question dealt Huygens.Centripetal acceleration formula proposed by them looks like:
Acs = (v * v) / r,
r - the radius of curvature of the distance traveled;v - velocity of movement.
The formula used to calculate the centripetal acceleration, still causes heated debate among enthusiasts.For example, recently it was announced curious theory.
Huygens, considering the system, based on the fact that the body is moving in a circle of radius R with velocity v, measured at the initial point A. Since the vector of inertia is directed at a tangent to the circle, it turns out the trajectory of a straight AB.However, the centripetal force keeps the body in the circle at point C. If we denote the center in O and draw a line AB, BO (total BS and CO), as well as stock, it turns out a triangle.In accordance with the law of Pythagoras:
OA = CO;
AB = t * v;
BS = (a * (t * t)) / 2, where a - acceleration;t - time (a * t * t - this is the speed).
If we now use the formula Pythagorean then:
R2 + t2 + v2 = R2 + (a * t2 * 2 * R) / 2+ (a * t2 / 2) 2, where R - radius, and the letter-to-digital spellingunsigned multiplication - degree.
Huygens admitted that, since the time t is small, it can not be taken into account in the calculations.Transforming the previous formula, it came to known Acs = (v * v) / r.
However, since the time taken in the box, there is a progression: the more t, the greater the error.For example, 0.9 is unaccounted for almost 20% of the final value.
concept of centripetal acceleration is important for modern science, but it is clear that this issue is still too early to finish.
