Acceleration in dynamics and kinematics is a physical magnitude that determines the change in velocity of an object in an interval of time. In the international system of units, we must express the value of this magnitude in meters per second squared (m/s 2 ).
In colloquial language, we speak of acceleration to refer to the increase in the speed of a body. However, this magnitude can be negative and implies a speed reduction. Thus, a positive acceleration entails an increase in speed. On the contrary, negative accelerations indicate a speed reduction. Finally, if the average acceleration is null, the velocity remains constant.
In kinematics calculations, it is important to establish a reference system. For example, the speed of a person walking inside a train is not the same for an observer inside the train as for an observer situated on the platform. Therefore, the reference system is the position of the observer.
Acceleration, like velocity, is a vector quantity. It means that it expresses magnitude and direction.
What Is the Acceleration of Free Fall?
The acceleration of a free-falling object is the acceleration due to gravity, which is the effect of gravity on moving objects. The direction is always from the object of study to the center of the Earth. At the surface of the Earth, the value of the gravitational constant acceleration is approximately 9.81 m/s 2.
The acceleration due to gravity is the manifestation of the universal attraction that drives bodies towards the center of the Earth. The acceleration due to gravity is denoted by q and is defined as the constant increase in velocity per unit of time perceived by a body in free fall. The magnitude of ge varies depending on the object's distance from the center of the Earth.
The acceleration due to gravity is not the same everywhere on the planet since the radius of the Earth is not the same everywhere. At the poles it is 9,832 m/s^2 and at the equator 9,7,780 m/s^2. By international convention, the normalized value of g = 9.806650 m/s^2 (32.17405 ft/s^2) is considered.
Examples of Free-fall Acceleration
For example, if we throw an object straight up without considering air resistance, over time, it will go up more slowly, stop, and start going down faster and faster. This variation in speed is due to the gravitational force.
This action is considered a uniformly accelerated rectilinear motion since the object does not change direction (only direction), and the acceleration is constant.
Another example is the satellites that orbit around our planet. The satellites experience a centripetal acceleration (gravity) that causes them to vary the direction of their speed and thus rotate around the earth.
What Is Instant Acceleration?
The instantaneous acceleration of a body is the one that the body has at a specific instant, at a certain point of its trajectory. To define instantaneous acceleration precisely, we can start from the average acceleration in an interval and make this infinitely small. This process is analogous to the one we followed with the average speed to calculate the instantaneous velocity.
Instantaneous acceleration is defined as the limit of the average acceleration when the considered time interval tends to 0. It is also defined equivalently as the derivative of velocity to time.
Instant acceleration measurement can be done with a data acquisition system and a simple accelerometer. Electronic accelerometers are manufactured to measure acceleration in one, two, or three directions. They have two conductive elements, separated by a material that varies its conductivity depending on the measurements, which will be related to the acceleration of the whole.
What Is the Difference Between Velocity and Acceleration?
Velocity is the physical magnitude that tells us the space traveled by an object for each fraction of time. For example, if a car travels at 30 m/s, the distance traveled will be 30 meters every second.
On the other hand, the acceleration indicates the speed variation for each fraction of time. So, in the same example, if at a specific moment, the car has an acceleration of 5m/s 2 , one second later, its speed will be 35m/s.
On the contrary, if the car's acceleration is non-existent, the vehicle moves in constant velocity.
What Is Normal or Centripetal Acceleration?
Centripetal acceleration affects the direction of an object's velocity.
The acceleration vector can have a different direction than the speed with which it moves. Therefore, this vector can be divided into two components:
Acceleration tangential to the movement of the object: it varies the absolute value of the body's speed.
Normal acceleration (perpendicular) to the body's movement: it is the component of the vector that changes the direction of the speed. This component is responsible for curvilinear movements.
What Is a Centrifugal Force?
Centrifugal force is an inertial force (also called "fictitious" or "pseudo-forces") that tends to move objects away from their center of rotation when they follow a circular motion.
Centrifugal force is an inertial force that acts on an object when a rotating reference system describes its motion.
Centrifugal force is the product of the reaction of an object that describes a circular path on the thing that causes this curvilinear motion, according to Newton's third law. So it is just the effect of inertia in a circular motion, not caused by the interaction of another physical body.
Centrifugal force arises when we analyze the motion of an object from a non-inertial or accelerated reference system that describes uniform circular motion.
Centrifugal force will be the product of mass by the centrifugal acceleration in a non-inertial reference system.
What Is the Relationship Between Acceleration and Force?
An object experiences an acceleration if there is some force acting on it.
This relationship is established by Newton's second law where it applies that:
F is the force (newtons)
m is the mass of an object (kilograms)
a is the acceleration of the object (meters per square meter)
Importance of Acceleration in Mechanical Engineering
Mechanical engineering is the design and manufacture of machines, that is, systems that perform movements. An important part is the sizing: the choice of actuators (jacks, motors) and components that support the forces.
If the masses set in motion or the accelerations are large. In that case, the dynamic effects - the forces necessary to create the accelerations or the forces resulting from the accelerations - are not negligible. Therefore, determining the instantaneous acceleration during a movement is essential for the parts to resist and to determine the energy consumption of the system.
In many cases, the specification is "to get an object from point A to point B in time t, with time t sometimes expressed as a rate (performing the move n times per hour). The design consists of:
Choose a technological solution to guide the movement.
Choose a technical solution to create the movement, control it, and transmit it (transmission).
Depending on the trajectory (therefore the technological solution for guidance), determine the laws of movement to meet the specifications (duration of the permissible movement), saving parts (limitation of efforts and therefore acceleration), and energy consumption.
According to the laws of motion, determine the necessary power and forces the parties are subjected to.
Dimension the system: choose the parts from the supplier's catalogs, or design them (select the materials, the sizes, draw them).