Each student is familiar with uniform movement, which for his description involves knowledge of only the value of the speed of the body. However, in nature, most often distributed uneven, accelerated movement. We consider in the article what acceleration is, why it arises when moving bodies, and we give acceleration formulas.
Historical study of the issue of movement
It's no secret that the world around us is in a state of constant movement and rotation. Despite this, the scientific study of the process of moving bodies in space began relatively recently. So, the philosophers of ancient Greece believed that movement is an unnatural state of objects (Zeno, Archimedes, Aristotle).
With the beginning of the Renaissance, as a result of the accumulation of experimental data, people began to change their views on the issue of movement. One of the first scientists in the world who proved that uniform rectilinear movement is a natural state of the surrounding bodies was Galileo. Subsequently, Isaac Newton expanded his ideas, creating a powerful and complete theory of the description of motion and its causes - classical mechanics.
Newton's second law and acceleration
From the first year of studying physics in schools, they begin to consider Newton's laws. They contain the answer to the question of why there is acceleration in bodies. We write the 2nd Newtonian law in the usual form:
F¯ = m * a¯.
Where does the formula for accelerating the body are written in the form:
a¯ = F¯ / m.
This expression means that the cause of the acceleration of bodies is an external force of absolutely any nature that acts on the bodies. The greater this force, the greater the importance of acceleration. On the other hand, the greater the mass of the body, the less acceleration a certain force can give it.
The written formula for the acceleration of the body contains one more important conclusion: the vector a¯ is directed in the same direction as the vector F¯, and the lengths of these vectors differ by the proportionality coefficient, which is the mass m.
Kinematics of motion with constant acceleration
The formula for accelerating motion was written above, however, no definition of this value was given. Acceleration in physics is the speed with which its speed changes during the movement of a body. Mathematically, this can be written as follows:
a = dv / dt.
Acceleration is the derivative of speed over time. This formula is valid for absolutely any kind of movement, including uneven and curvilinear movement, for example, rotation around a circle.
If the body moves with constant acceleration, and its initial speed is zero, then the following formulas are valid:
v = a * t;
S = a * t 2/2.
Both expressions are the basic formulas for the kinematics of uniformly accelerated motion, that is, such a movement of the body at which its acceleration is a constant.
In addition to accelerated motion, it is often necessary to solve problems of equally slow motion, which occurs when braking bodies. In this case, the following formulas are valid:
v = v 0 - a * t;
S = v 0 * t - a * t 2/2.
Here v 0 is the speed of the body until the moment when braking began.
It is easy to obtain the corresponding expression for acceleration from the formulas presented. So, in the case of equally slow movement we get:
a = (v 0 - v) / t;
a = 2 * (v 0 * t - S) / t 2 .
Circular rotation and acceleration
Unlike rectilinear movement, during rotation, not only the module changes, but also the direction of speed. Taking the time derivative of it, we can get two different components of the full acceleration, they are called tangential and normal accelerations (a t and a n ).
The tangential acceleration formula does not differ from the above, that is:
a t = dv / dt.
The quantity a t describes a change in the absolute value of the velocity and is directed along the tangent to the trajectory (circle).
Normal acceleration a n describes a change in the velocity vector, and not its absolute value. It is directed to the center of curvature of the trajectory (to the center of the circle), therefore it is also called centripetal. The formula for its calculation is:
a n = v 2 / r.
Where r is the radius of curvature of the trajectory. As this equality shows, for the appearance of a n it is enough that the velocity vector changes its direction, while the velocity itself can remain constant. A striking example of uniform motion in a circle with a certain centripetal acceleration is the rotation of our Earth around an axis or around the Sun.
Acceleration of gravity
This acceleration is denoted by the letter g in physics. Its appearance is associated with the action of gravity or gravity of massive objects (planets, stars, galaxies). As applied to our Earth, we can say that it tells all bodies during their fall near the surface an acceleration of 9.81 m / s 2 (for every second the speed increases by 9.81 m / s).
In reality, this fact is difficult to observe on light objects, since the force of air resistance acts on them when they fall.
In terms of body weight P, the acceleration formula g will take the form:
g = P / m.
Through the kinematics equation of uniformly accelerated motion, the acceleration g can be calculated as follows:
h = g * t 2/2 =>
g = 2 * h / t 2 .
Where h is the height of the fall of the body. Galileo used the last formula to experimentally determine the value of g.