When solving problems in physics, it is often necessary to derive working formulas taking into account the provided condition. One of the most reliable checks of the correctness of the obtained formula is the coincidence of the units in the right and left parts of the equality. In this article, we will consider the question of what acceleration is measured in.
What is acceleration?
We immediately give a definition of this quantity, and then explain its features. Acceleration is understood to mean the speed with which the speed changes at each moment of time when the body moves. Since speed is a vector quantity, its modulus and direction can change. Both types of change are described by the concept of acceleration.
To determine the instantaneous acceleration, the following expression is used:
a¯ = dv¯ / dt.
Taking the first time derivative of velocity, we obtain the dependence of acceleration on t.
In addition to instantaneous acceleration (the value of a¯ at a particular point in time), average acceleration is often used in practice. It is defined as follows:
a cp ¯ = Δv¯ / Δt.
Here Δv¯ is the velocity difference at the end and at the beginning of the time interval Δt. In contrast to the instantaneous value, the average acceleration characterizes the entire process of motion, so in practice it is more useful. Obviously, if Δt-> dt, then a cp ¯-> a¯.
How is acceleration measured?
It is easy to answer this question if we consider the formulas written in the previous paragraph for the instantaneous and average values. As you know, the speed is determined in meters per second (m / s). Of course, you can use other units of measure for v¯, for example, kilometers or miles per hour, but we are talking about units of the international SI system. SI time is measured in seconds (c). Taking the ratio of these quantities, we come to the answer to the question of what is the acceleration measured. Its units are meter per square second or abbreviated m / s².
What does the record mean: a = 1 m / s²? This means that for every second of movement, the body increases its speed by 1 m / s.
The following are other possible units of measure for acceleration, however m / s² is the base, and all other units are reduced to it.
Strength and Acceleration
The mathematical definition of acceleration described above does not contain any information about where it comes from and what causes bodies to accelerate. The answers to these questions can be understood if we recall what the second law of Newton consists of. It says that as soon as a nonzero external force F¯ appears, acting on a body of mass m, it inevitably leads to the appearance of acceleration a¯. The corresponding expression is written as:
F¯ = m * a¯.
We can, using this formula, determine what acceleration is measured in this case. Strength is expressed in Newtons, and mass in kilograms, then we get:
a¯ = F¯ / m [N / kg].
Newton is not the basic unit in the SI system, so N / kg is rarely used in tasks to express acceleration. Nevertheless, this unit can be found in some problems of motion dynamics.
Circular motion
We specifically highlighted in a separate paragraph of the article the issue of moving the body around the circumference. The fact is that during rotation around a certain axis, not only the absolute value of the body velocity can change, but also its direction. This type of movement leads to the appearance of two acceleration components in the body: normal or centripetal and tangential or tangent.
The tangent component describes the change in the module v¯; therefore, the unit m / s² is used for it. However, rotation is often described in angular terms. Angular acceleration is expressed in radians per second squared (rad / s²). Recall that a radian is a measure of an angle that relies on an arc of one radius of a circle.
As for the centripetal acceleration component, the following formula is used to calculate it:
a c = v² / r.
Where r is the radius of rotation. What is centripetal acceleration measured in? We substitute the corresponding units for v and r into this expression, we get:
a c = [m² / s² / m] = [m / s²].
Thus, normal acceleration is measured in the same units as full acceleration (m / s²).
Free fall acceleration measurement
This acceleration (it will be denoted by the letter g) occurs due to the action on all the bodies that surround us, the gravity of the Earth. The average value of g on our planet is 9.81 m / s², nevertheless, this value varies by several percent depending on the terrain.
The science that deals with measuring g is called gravimetry. Answering the question of which instrument measures acceleration, it should be said that this is either an absolute or relative gravimeter. An absolute gravimeter measures g in the forehead, calculating the time a body falls in an airless space from a certain height. A relative gravimeter is a spring with a load whose elongation is calibrated according to some known acceleration g in a given area.
Using a gravimeter, gravity acceleration is measured in galls. This unit is named after Galileo, who for the first time in history used a mathematical pendulum to calculate the acceleration g. One gal is equal to the hundredth of m / s².
The measurement of g in a given area is carried out with the aim of analyzing the composition of the rocks, while searching for minerals or groundwater. Gravimeters are also used in archeology and seismology.