Acceleration

The acceleration (also known as linear acceleration ) is the physical quantity characterizing the speed with which varies the speed of a particle. It is a vector magnitude , so it is totally determined by the properties that identify it: its magnitude, direction and direction.

Summary

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  • 1 Denotation
  • 2 Equation
  • 3 Acceleration in Kinematics
  • 4 Signs of acceleration
  • 5 Acceleration in Dynamics
  • 6 Examples of the concept of acceleration
  • 7 Measurement of acceleration
  • 8 Acceleration in relativistic mechanics
  • 9 Sources
  • 10 Bibliographies

Denotation

It is denoted by the letter (a). In the International System of Units (SI) it is expressed in meters / second squared (m / s²), while in the Cegesimal System of Units (CGS) it is measured in centimeters / second squared (cm / s²). Acceleration are units of speed per unit of time, or the dimensions of acceleration are L / T², in other words, units of length (L) per unit of time (T) raised to the second power in the denominator. Examples of frequently used acceleration units are: m / s², km / h² and cm / s².

In summary, the units of acceleration are:

International system:

1 m / s2

Cegesimal system:

1 cm / s2 = 1 Gal

The Gal is the name assigned to the acceleration unit in the Cegesimal System, that is, to the centimeter per second at -2 (cm.s-2). The symbol for this unit is Gal. This name was given in honor of Galileo Galilei , who was the first to measure the acceleration of gravity . It is an unusual unit, because it does not belong to the International System of Units. The gravitational acceleration of the Earth varies between 976 and 983 Gal.

By definition:

1 Gal = 1 cm.s-2.

Its equivalence with the SI unit is:

1 Gal = 0.01 ms-2

 

Equation

The following formula is used to determine the value of acceleration :

a = (velocity variation) / time interval

that is to say,

a = (ΔV / Δt) = (V – Vo) / t

In this formula, Vo means the initial velocity of the particle and V its final velocity reached at time t. When the particle’s initial velocity is zero (that is, the particle starts from the state of rest Vo = 0), then the acceleration formula is reduced to:

a = V / t

Acceleration in Kinematics

  1. If the particle is moving with constant speed in a straight line ( Uniform Rectilinear Motion,or MRU ), then its acceleration is zero.
  2. If the acceleration of the particle moving in a straight line is constant and different from zero, then said particle is said to be animated by a Uniformly Varied Rectilinear Movementor MRUV (in this movement the acceleration coincides with the direction of the velocity of the particle at each point of the path).
  3. The acceleration of a particle can take values ​​greater than zero (a> 0, that is, positive in relation to the speed direction), less than zero (a <0, negative in relation to the speed direction) and even equal to zero. When the particle moves with constant acceleration greater than zero, the particle’s motionis said to be uniformly accelerated and the particle’s velocity increases over time. If the particle moves with constant acceleration less than zero, then the particle’s motion is uniformly retarded and the particle’s speed decreases as time passes. Particles with acceleration equal to zero are at rest or moving with constant speed.
  4. In the case of a curvilinear movement, the acceleration produces a variation of the modulus and the direction of the velocity vector, that is, the acceleration represents for the velocity vector the same as the velocity for the position vector .

Signs of acceleration

If the speed increases in module we say that the movement is accelerated , on the other hand if the speed decreases in module we say that the movement is decelerated . In accelerated motion, acceleration and velocity have the same direction. On the other hand, if the movement is decelerated, the acceleration has the opposite direction (opposite direction) to the speed. In the Vertical Free Fall Movement : when the body ascends it decelerates. When the body descends it accelerates.

Acceleration in Dynamics

In Newtonian mechanics, for a body with constant mass , the acceleration of the body is directly proportional to the force acting on itself and inversely proportional to its mass ( Newton’s Second Law ):

(F) is the resulting force acting on the body, (m) is the mass of the body, and (a) is the acceleration.

The previous relation is valid in any inertial reference system .

According to Newtonian mechanics, a particle cannot follow a curved path unless a certain acceleration acts on it as a consequence of the action of a force, since if it did not exist, its movement would be rectilinear. Also, a particle in rectilinear motion can only change its speed under the action of an acceleration in the same direction as its speed (directed in the same direction if it accelerates; or in the opposite direction if it decelerates). In short: an object is only accelerated if a force is applied to it. According to Newton’s Second Law of Motion , the change in velocity is directly proportional to the applied force. Example: A falling body is accelerated by the Force of gravity .

Examples of the concept of acceleration

  1. The acceleration of gravity(g) on ​​Earth is the acceleration produced by the Earth’s gravitational force ; its value on the Earth’s surface, in a Free Fall Movement, is the same for all bodies, whatever their mass when it is possible to neglect the resistance of the air, it is approximately 9.8 m / s². At the poles: g = 9.83 m / s² (Maximum) and in Ecuador: g = 9.78 m / s² (Minimum)
  2. The average accelerationis defined as the quotient of a = V / t.
  3. The instantaneous acceleration, is defined as the limit to which the incremental ratio tends Dv / Dt where Dt → 0; this is the derivative of the velocity vector with respect to time.
  4. The centripetal acceleration.
  5. The angular acceleration, is defined as the change of the angular velocity , that is, a change in the rate of rotation or the direction of the axis.

Acceleration measurement

Acceleration measurement can be done with a data acquisition system and a simple accelerometer .

Acceleration in relativistic mechanics

  • Special relativity:

The analogue of acceleration in relativistic mechanics is called quadriaceleration and is a quadrivector whose three spatial components for small speeds coincide with those of Newtonian acceleration (the temporal component for small speeds is proportional to the power of the force divided by the speed of the light and the mass of the particle).

A Quadrivector is the mathematical representation in the form of a four-dimensional vector of a magnitude.

  • General relativity:

In the general theory of relativity the case of acceleration is more complicated, since because space-time itself is curved (see image below: curvature of space-time), a particle on which no force acts it can follow a curved path, in fact the curved line that follows a particle on which no external force acts is called the Geodetic Line .

 

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