I want all the dimensions formulae in physics.
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The dimension of a physical quantity is defined as the power to which the fundamental quantities are raised to express the physical quantity. The dimension of mass, length and time are represented as [M], [L] and [T]respectively. For example
We say that dimension of velocity are, zero in mass, 1 in length and -1 in time.
Dimensional formula of a Physical Quantity
The dimensional formula is defined as the expression of the physical quantity in terms of its basic unit with proper dimensions. For example, dimensional force is
F = [M L T-2]
It's because the unit of Force is Netwon or kg*m/s2
Dimensional Formula of some Physical Quantities
Dimension formula of a physical quantity can only be written when its relation with other physical quantities is known. Some of the physical quantities with the dimensional formula are given below
Dimensional equation
An equation containing physical quantities with dimensional formula is known as dimensional equation. Dimensional equation is obtained by equating dimensional formula on right hand side and left hand side of an equation.
Principle of Homogeneity of Dimensional Equation
According to this principle, the dimensions of fundamental quantities on left hand side of an equation must be equal to the dimensions of the fundamental quantities on the right hand side of that equation. Let us consider three quantities A, B and C such that C = A + B. Therefore, according to this principle, the dimensions of C are equal to the dimensions of A and B. For example:
Dimensional equation of v = u + at is:
[M0 L T-1] = [M0 L T-1] + [M0 L T-1] X [M0 L0 T] = [M0 L T-1]
Uses of Dimensional Equations
The dimensional equations have got the following uses:
To check the correctness of a physical relation.
To derive the relation between various physical quantities.
To convert value of physical quantity from one system of unit to another system.
To find the dimension of constants in a given relation.
Limitation of Dimensional analysis
Following are the limitations of the dimensional analysis.
It does not give information about the dimensional constant.
if a quantity depends on more than three factors having dimension, the formula cannot be derived.
We cannot derive the formulae containing trigonometric function, exponential functions, logarithmic function, etc.
The exact form of relation cannot be developed when there are more than one part in any relation.
It gives no information whether a physical quantity is scalar or vector.
Submitted by Terence Dangol
We say that dimension of velocity are, zero in mass, 1 in length and -1 in time.
Dimensional formula of a Physical Quantity
The dimensional formula is defined as the expression of the physical quantity in terms of its basic unit with proper dimensions. For example, dimensional force is
F = [M L T-2]
It's because the unit of Force is Netwon or kg*m/s2
Dimensional Formula of some Physical Quantities
Dimension formula of a physical quantity can only be written when its relation with other physical quantities is known. Some of the physical quantities with the dimensional formula are given below
Dimensional equation
An equation containing physical quantities with dimensional formula is known as dimensional equation. Dimensional equation is obtained by equating dimensional formula on right hand side and left hand side of an equation.
Principle of Homogeneity of Dimensional Equation
According to this principle, the dimensions of fundamental quantities on left hand side of an equation must be equal to the dimensions of the fundamental quantities on the right hand side of that equation. Let us consider three quantities A, B and C such that C = A + B. Therefore, according to this principle, the dimensions of C are equal to the dimensions of A and B. For example:
Dimensional equation of v = u + at is:
[M0 L T-1] = [M0 L T-1] + [M0 L T-1] X [M0 L0 T] = [M0 L T-1]
Uses of Dimensional Equations
The dimensional equations have got the following uses:
To check the correctness of a physical relation.
To derive the relation between various physical quantities.
To convert value of physical quantity from one system of unit to another system.
To find the dimension of constants in a given relation.
Limitation of Dimensional analysis
Following are the limitations of the dimensional analysis.
It does not give information about the dimensional constant.
if a quantity depends on more than three factors having dimension, the formula cannot be derived.
We cannot derive the formulae containing trigonometric function, exponential functions, logarithmic function, etc.
The exact form of relation cannot be developed when there are more than one part in any relation.
It gives no information whether a physical quantity is scalar or vector.
Submitted by Terence Dangol
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there are total of 7 diminesion in physicsDimension, in physics, of a physical quantity is the index of each of the fundamental quantity ( Length, mass, time, temperature, Luminous intensity, Current ) which expresses that quantity.
For example, the dimension of speed can be derived in the following way:
Speed= distance/time
= length/time
= L/T
= L.T^-1.
The above expression tells you the dimension of "speed".
In its dimension, there is no mention of mass, current or temperature because they don't play any role in defining this quantity. Or, you could say the dimension of mass in this expression is zero, that of current , luminous intensity, temp too is zero.
In a completely different sense, dimension is about the space an object takes up. It signifies length, breadth, and height/thickness of the physical object which occupies space.
So the dimensions of a brick could be expressed as 20cm*10cm*6cm.
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Peter Bulyaki, Software Engineer (2004-present)
Answered Thu
If physicists knew exactly what a dimension is in nature they would know a lot more about the universe, but unfortunately this question is still waiting to be answered correctly. Which means you are asking a very good question.
A dimension provides a degree of freedom along which events are prevented from happening in the same place and at the same time. Mechanisms that make various forms of energy appear as mass (Higgs, QCD) are likely to be responsible for creating probabilities other than 0 and 1 for us to observe massive particles separately in space, to observe them moving and interacting with each other. It seems though that dimensions (space and time) are both the creators of particles, and are also created by particles.
From General Relativity we know for example that every moving observer has its own clock, so at least we have proof that time is not universal. From the curvature of spacetime and how it behaves in the presence of mass it seems likely that space itself is not universal either, but rather bound to the quantum probabilities that describe the possible locations of particles.
For example, the dimension of speed can be derived in the following way:
Speed= distance/time
= length/time
= L/T
= L.T^-1.
The above expression tells you the dimension of "speed".
In its dimension, there is no mention of mass, current or temperature because they don't play any role in defining this quantity. Or, you could say the dimension of mass in this expression is zero, that of current , luminous intensity, temp too is zero.
In a completely different sense, dimension is about the space an object takes up. It signifies length, breadth, and height/thickness of the physical object which occupies space.
So the dimensions of a brick could be expressed as 20cm*10cm*6cm.
4.3k Views · View Upvoters
Your feedback is private.
Is this answer useful?
Upvote · 12
Comment...
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Peter Bulyaki, Software Engineer (2004-present)
Answered Thu
If physicists knew exactly what a dimension is in nature they would know a lot more about the universe, but unfortunately this question is still waiting to be answered correctly. Which means you are asking a very good question.
A dimension provides a degree of freedom along which events are prevented from happening in the same place and at the same time. Mechanisms that make various forms of energy appear as mass (Higgs, QCD) are likely to be responsible for creating probabilities other than 0 and 1 for us to observe massive particles separately in space, to observe them moving and interacting with each other. It seems though that dimensions (space and time) are both the creators of particles, and are also created by particles.
From General Relativity we know for example that every moving observer has its own clock, so at least we have proof that time is not universal. From the curvature of spacetime and how it behaves in the presence of mass it seems likely that space itself is not universal either, but rather bound to the quantum probabilities that describe the possible locations of particles.
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