The key to success in solving physics problems is a clear understanding of the meaning of the quantity to be found. Knowledge of a specific formula is not sufficient to solve practical problems, since many of them do not involve the use of a specific mathematical relationship between quantities. This dependence must be obtained independently. In this article, we explain what the physical meaning of acceleration is.
Motion kinematics
The scientific approach to the study of motion in physics began to be applied not so long ago. In XVII, thanks to the achievements of scientists such as Galileo Galilei and Isaac Newton, mankind finally learned how to predict the behavior of bodies during their movement using a mathematical apparatus.
Kinematics is one of two important branches of physics (the second is dynamics), which uses a scientific approach to describing the characteristics of motion. In kinematics, they do not focus on the reasons for the beginning of the movement of objects. Its main task is to determine the coordinates of the body at any time. To solve this problem, kinematics has a set of characteristics related to the equations. The main characteristics are the path traveled, speed and acceleration. The physical meaning of the latter quantity will be considered later in the article.
Acceleration Definition
As you know, the speed of a path is described in physics by speed. If it is denoted by the letter v, and the path is denoted by the letter l, then the following expression can be written:
v = dl / dt.
It is simple to calculate the velocity modulus at time t if we find the time derivative of the function l (t). The acceleration is obtained if we find this derivative, but from the function v (t), that is:
a = dv / dt.
This equality indicates that the physical meaning of acceleration consists in the speed of change in time of the speed of the body.
Acceleration - Vector Feature
Speed is a vector that is tangent to the line along which the body moves. The time derivative of a vector is also a vector, that is, acceleration is a vector characteristic. However, its direction has nothing to do with the velocity vector v. The acceleration a is directed to where the velocity change vector is. For example, in the case of a rectilinear movement of the bodies of the vector, the values of a and v will always lie on one straight line, therefore, there are two possible options for their relative orientation:
- they are directed in one direction;
- they are directed opposite each other.
In the first of these cases, the body increases its speed, that is, it accelerates. In the second case, the body is inhibited.
In the case of curvilinear motion, the function v (t) changes not only in absolute value, but also in direction. Acceleration describes both types of changes in speed; therefore, its vector is directed at a certain angle to the vector of magnitude v. A classic example is circular motion uniformly. The velocity modulus in this case remains constant, but its vector changes. As a result, the corresponding acceleration will be directed to the center of the circle. It is called normal or centripetal.
Angular acceleration
The above was an example of uniform circular motion. In the general case, the speed of a moving body changes modulo depending on time. To this end, in physics it is customary to decompose the full acceleration a into tangential a t and normal components a n . The first describes the change in speed in magnitude, the second - in direction.
In the case of accelerated movement around a circle, the body rotates around an axis. It is convenient to use angular kinematic characteristics to describe this type of motion: the angle of rotation θ, angular velocity ω, and angular acceleration α. These quantities are related by the following equalities:
ω = dθ / dt;
α = dω / dt.
The angular velocity shows at what angle the body rotates around its axis in radians in one second. The meaning of physical angular acceleration is that it shows how fast the quantity ω changes. For example, if α = -1 rad / s 2 , then this means that the speed decreases by 1 rad / s for every second.
The angular kinematic characteristics are associated with the corresponding linear quantities by the following relationships:
v = ω * r;
a t = α * r.
Both equalities indicate the convenience of using angular quantities to describe the motion of rotation. Unlike linear quantities, they are independent of radius r. Please note that angular acceleration is different from zero only if the body has some tangential acceleration.
Free fall
In physics, free fall is understood only by the action of gravity as the motion of bodies. This force is calculated by the following formula:
F = m * g.
Here m is the inertial mass of the body, g is a constant value near the surface of the planet Earth. It is called the acceleration of gravity. The physical meaning of acceleration is as follows: if the body falls freely vertically downward, then for every second of its movement its speed will increase by 9.81 m / s. Conversely, if a body is thrown vertically upwards, then its speed will decrease by g every second. If the beginning of the motion of the body is carried out at a certain angle to the horizon, then the reasoning above is valid only for the vertical component of the total speed.