Dimension Of Acceleration

Dimension Of Acceleration: The rate of change of position of an object in any direction/path is known as speed and is measured by distance upon time taken. Speed has the dimension LT^{– 1} and acceleration LT^{– 2}. Since speed has the dimension [M⁰ L¹ T^-1] and length is measured in ‘m’ and time is measured in ‘s’, so ‘m/s’ becomes the unit of speed. The size of a derived unit such as speed, which is the distance (length) divided by time, becomes [M⁰ L¹ T^-1] in this notation.

Dimension of mass over acceleration

Observing, and interpreting u(t) as displacement, we understand that the term mu (mass over acceleration) has the dimension [M⁰ L¹ T^-2]. The magnitude of the force, another derived unit, is the same as the magnitude of the length, and thus the magnitude of the force is [M⁰ L¹ T^-2]. When making a choice, mass is determined (not a base measurement) by dividing the force by the gravitational acceleration (which has length divided by the square of time).

Let’s understand what is acceleration?

• Acceleration is the rate at which velocity/speed changes with time, in terms of both speed and direction. A point or an object moving in an uncurved line is accelerated if it speeds up or slows down. Movement on a circle is accelerated even if the speed is constant because the direction is always changing. For all remaining sorts of motion, both effects contribute to the acceleration.
• We know that acceleration is a vector quantity so it has both a magnitude and a direction. Velocity is likewise a vector quantity. Acceleration is characterized as the change in the velocity vector in a time interval, divided by the time interval.

Fluid Mechanics

In fluid mechanics, we usually choose length, mass, time, and temperature as the main measurements. The length measurement is written as [L], the mass measurement as [M], the time measurement as [T], and the temperature measurement as θ (other base units are simply omitted). as we do not use them in this text). Force [f] has one mass dimension, one length dimension, and minus two (-2) time dimensions.

One-dimensional Motion

Meanwhile, the space force formula = [M1 L¹ T^-2] takes the mass as the equation. Gravitational acceleration (g) = force x [Mass^-1] . Take this as an equation. In the one-dimensional motion part of constant acceleration, we learned that this acceleration is given by g = 9.8 m/s.

Derivation of the dimension of acceleration

In order to derive the dimensional formula for acceleration, we need to derive formulas for displacement and velocity, two quantities on which acceleration depends. From the measurement equation above, acceleration over time has one dimension of length minus two (-2) dimensions, and no mass dimension.

Also Check: The Moment of Inertia

Dimensional Equation

• The dimension equation for speed is [M⁰ L¹ T^-1], and 0, 1, -1 are called dimensions. An expression that gives the relationship between derived units and base units in terms of size is called a dimensional equation.
• The force to which the basic units reach the unity of a physical quantity is called the magnitude of this physical quantity. The unit of physical quantity follows from the dimensional expression.

Homogeneity Principle of Measurement

• Using the principle of dimensional uniformity, new relationships between physical quantities can be derived if the relevant quantities are known. An equation is dimensionally correct if, in a given relationship, the terms on both sides have the same dimensions. This concept is better known as the Homogeneity Principle of Measurement.
• All units of the same size are related to each other using a conversion factor (for example, 2.54 cm is exactly equal to 1 inch by definition). It is important to note that there can be many units used to describe a measurement. Dimensions and units are commonly confused, although the solution to all engineering problems must include units.

Dimensions of ordinary physical quantity

Dimensions of ordinary physical quantity P. Many derived quantities are measured in derived units, which have their own names. A dimension is a physical quantity that can be measured, while a unit is an arbitrary name associated with a particular dimension, measured relative to an agreed-upon definition (e.g. dimension is length, a meter is a relative unit for describing length). Different physical quantities like m, u(t), b and k have different dimensions and are measured in different units, but mu, bu and ku must be the same size, otherwise there is no point in adding them. For more complex physical quantities, knowledge of formulas in other dimensions may be required.

Square brackets [], A will denote the magnitude of the quantity, for example, for speed we write [v] = LT^{– 1}. The next task is to put this combination, which in turn has the dimension MLT^{– 2} .

L^{– 2} / ML^{– 1} T ^{– 1} = L ^{– 1} T^-1, together with [a] = L, to get a value with flow dimensions, L³ T^{– 1}.

How can dimensional thinking help us to find the range of AI through a pipe?

Well, the flow itself, say, in cubic meters per second, has the dimension [I] = M³ T ^{– 1}.

For example, acceleration can be expressed in meters per second squared (ms^-2) or feet per second squared (ft-s^-2), while speed can be expressed in meters per second (ms^-1) or kilometers (km). (h^-1). Acceleration [a] can be defined as the rate of change in speed [v] over time. If the object is moving at a constant speed, then the plot of distance versus time x vs. t shows the same position change in any time interval.

Significance of Dimension Of Acceleration in IIT JEE exam

It is critical to take a holistic approach to every facet of a subject’s chapter. It will not only adequately prepare you for the exam, but will also clarify your understanding of each topic. It will help you in JEE preparation and answer conceptual problems in the exam. The number of questions from the chapter unit and dimensions would be one or two, with a weightage of roughly four marks.