What is acceleration?
Let us consider in more detail what acceleration is in physics? This is a message to the body of additional speed per unit of time. In the International System of Units (SI), the number of meters passed per second (m / s) is considered to be the unit of acceleration. For the off-system unit of measurement Gal (Gal), which is used in gravimetry, the acceleration is 1 cm / s2.
Types of acceleration
What is the acceleration in the formulas. The type of acceleration depends on the motion vector of the body. In physics, this can be a movement in a straight line, in a curve, and in a circle.
- If the object moves in a straight line, the movement will be equally accelerated, and linear accelerations will begin to act on it. The formula for its calculation (see formula 1 in Fig.): A = dv / dt
- In the case of a body moving in a circle, the acceleration will consist of two parts (a = at+ an): tangential and normal acceleration. Both are characterized by the speed of the subject. Tangential - change in speed modulo. Its direction is tangential to the trajectory. This acceleration is calculated by the formula (see. Formula 2 in Fig.): At= d | v | / dt
- If the speed of the object on a circle is constant, the acceleration is called a centripetal or normal. The vector of such acceleration is constantly directed to the center of the circle, and the value of the modulus is equal (see formula 3 in Fig.): | A (vector) | = w2r = v2/ r
- When the velocity of the body around the circumference is different, angular acceleration occurs. It shows how the angular velocity has changed per unit of time and is equal to (see formula 4 in the figure): E (vector) = dw (vector) / dt
- In physics, options are also considered when the body moves in a circle, but at the same time approaches or moves away from the center. In this case, the object is acted upon by Coriolis accelerations. When the body moves along a curved line, its acceleration vector will be calculated using the formula (see formula 5 in Fig.): A (vector) = aTT + ann (vector) + abb (vector) = dv / dtT + v2/ Rn (vector) + abb (vector), in which:
- v - speed
- T (vector) is the unit vector tangent to the trajectory along the velocity (tangent ort)
- n (vector) - ort of the main normal relative to the trajectory, which is defined as a unit vector in the direction dT (vector) / dl
- b (vector) - ort binormal relative to the trajectory
- R is the radius of curvature of the trajectory
In this case, the binormal acceleration abb (vector) is always zero. Therefore, the final formula looks like this (see formula 6 in Fig.): A (vector) = aTT + ann (vector) + abb (vector) = dv / dtT + v2/ Rn (vector)
What is gravitational acceleration?
The acceleration due to gravity (indicated by the letter g) is called acceleration, which is given to an object in a vacuum by gravity. According to Newton's second law, such acceleration is equal to the force of gravity, which acts on an object of a single mass.
On the surface of our planet, the value of g is called 9.80665 or 10 m / s². To calculate the real g on the surface of the earth, several factors will have to be taken into account. For example, latitude and time of day. So the true g value can be from 9.780 m / s² to 9.832 m / s² at the poles. An empirical formula is used for its calculation (see formula 7 in Fig.), In which φ is the breadth of the terrain, and h is the distance above sea level, expressed in meters.
Formula for calculating g
The fact is that such an acceleration of free fall consists of gravitational and centrifugal acceleration. The approximate gravitational value can be calculated by representing the Earth as a homogeneous ball with mass M, and calculating the acceleration over its radius R (formula 8 in rice, where G is a gravitational constant with a value of 6.6742 · 10−11m³s−2kg−1).
If you use this formula to calculate the gravitational acceleration on the surface of our planet (mass M = 5.9736 · 1024kg, radius R = 6,371 · 106m), we get the formula 9 in rice, however, this value conditionally coincides with the fact that such speed, acceleration in a particular place. The inconsistencies are due to several factors:
- Centrifugal acceleration, which takes place in the reference system of rotation of the planet
- The fact that the planet Earth is not a spherical shape
- The fact that our planet is heterogeneous
Acceleration Measuring Instruments
Acceleration is usually measured with an accelerometer. But he does not calculate the acceleration itself, but the force of the support reaction that occurs during accelerated motion. The same resistance forces appear in the field of gravity, so the accelerometer can measure gravity.
There is another accelerometer, the accelerograph. It calculates and graphically records the values of the acceleration of translational and rotational motion.
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