Movement is one of the main properties of the world in which we live. It is known from physics that all the bodies and particles of which they are composed constantly move in space even at an absolute zero temperature. In this article, we consider the definition of acceleration as an important kinematic characteristic of mechanical motion in physics.
What size are we talking about?
According to the definition, acceleration is a quantity that allows you to quantitatively describe the process of changing speed from time to time. Mathematically, acceleration is calculated as follows:
a¯ = dv¯ / dt.
This formula for determining acceleration describes the so-called instantaneous value a¯. To calculate the average acceleration, you should take the ratio of the difference in speeds to a longer period of time.
The quantity a¯ is a vector. If the speed is directed along the tangent to the considered path of the body, then the acceleration can be directed in a completely arbitrary way. It has nothing to do with the trajectory of movement and with the vector v¯. Nevertheless, both of these motion characteristics depend on acceleration. This is because ultimately it is the acceleration vector that determines the trajectory and velocity of the body.
To understand where the acceleration a¯ is directed, one should write the second Newtonian law. In a well-known form, it looks like this:
F¯ = m * a¯.
Equality means that two vectors (F¯ and a¯) are connected to each other through a numerical constant (m). From the property of vectors it is known that multiplication by a positive number does not change the direction of the vector. In other words, acceleration is always directed towards the action of the total force F¯ on the body.
The measured value is measured in meters per square second. For example, the gravitational force of the Earth near its surface gives the bodies an acceleration of 9.81 m / s 2 , that is, the speed of a freely falling body in airless space increases by 9.81 m / s for every second.
The concept of uniformly accelerated movement
The formula for determining acceleration in the general case was written above. However, in practice, it is often necessary to solve problems for the so-called uniformly accelerated movement. It is understood as such a movement of bodies in which their tangential component of acceleration is a constant. We emphasize the importance of constancy of the tangential rather than normal component of acceleration.
The full acceleration of the body in the process of curvilinear motion can be represented in the form of two components. The tangential component describes a change in the velocity modulus. The normal component is always directed perpendicular to the trajectory. It does not change the modulus of speed, but it changes its vector.
Below we will reveal a somewhat more detailed question regarding the acceleration component.
The movement is uniformly accelerated in a straight line
Since the velocity vector does not change when moving in a straight line of the body, the normal acceleration is zero. This means that the full acceleration is formed exclusively by the tangential component. The definition of acceleration with uniformly accelerated movement is carried out according to the following formulas:
a = (v - v 0 ) / t;
a = 2 * S / t 2 ;
a = 2 * (Sv 0 * t) / t 2 .
These three equations are the basic expressions of kinematics. Here v 0 is the speed that the body had before acceleration. It is called primary. The value S is the path traveled by the body along a straight path in time t.
Whatever value of time t we substitute in any of these equations, we always get the same acceleration a, since it does not change in the process of the type of motion under consideration.
Accelerated rotation
Moving around a circle with acceleration is a fairly common type of movement in technology. To understand this, just remember the rotation of the shafts, discs, wheels, bearings. To determine the acceleration of a body with uniformly accelerated circular motion, angular values are often used, not linear ones. Angular acceleration, for example, is defined as follows:
α = dω / dt.
The value of α is expressed in radians per second squared. This acceleration with the tangential component of a is related as follows:
α = a t / r.
Since α is constant during uniformly accelerated rotation, the tangential acceleration a t directly proportionally increases with increasing radius r of rotation.
If α = 0, then there is only a nonzero normal acceleration during rotation. Nevertheless, this movement is called equally variable or uniform rotation, and not uniformly accelerated.