Dimensional formulas provide essential relationships between physical quantities, helping students and professionals in physics and engineering understand how different units interact. This resource outlines the dimensional formulas for various physical quantities, including area, volume, mass density, force, energy, and more. Ideal for students preparing for exams in physics or engineering, it serves as a quick reference for understanding key concepts in dimensional analysis. The document includes detailed formulas and explanations, making it a valuable tool for both study and practical application.

Key Points

  • Details the dimensional formulas for area, volume, and mass density.
  • Explains the relationships between force, energy, and work in dimensional terms.
  • Covers key physical quantities like velocity, acceleration, and momentum.
  • Includes formulas for pressure, stress, and strain relevant to engineering applications.
AARYAN KHAIRE
5 pages
Language:English
Type:Resource
Biology
AARYAN KHAIRE
5 pages
Language:English
Type:Resource
Biology
209
/ 5
Dimensional Formulae of Physical Quantities
S.No Physical Quantity Relationship with other
physical quantities
Remark Dimensional
Formula
1. Area
Length × breadth
[M
0
L
2
T
0
]
2. Volume
Length × breadth × height
[M L
3
T
0
]
3. Mass density Mass/volume [M L
–3
T
0
]
4. Frequency 1/time period [M
0
L
0
T
–1
]
5. Velocity, speed Displacement/time [M
0
L T
–1
]
6. Acceleration Velocity/time [M
0
L
T
–2
]
7. Force
Mass × Acceleration
[M L T
–2
]
8. Impulse
Force × Time
[M L T
–1
]
9. Work, Energy
Force × Distance
[M L
2
T
–2
]
10
.
Power Work/Time [M L
2
T
–3
]
11
.
Momentum
Mass × Velocity
[M L T
–1
]
12
.
Pressure, stress Force/Area [M L
–1
T
2
]
13
.
Strain
dimension Original
dimensionin change
[M
0
L
0
T
0
]
14
.
Modulus of elasticity Stress/Strain [M L
–1
T
–2
]
15
.
Surface tension Force/Length [M L
0
T
–2
]
16
.
Surface energy Energy/Area [M L
0
T
–2
]
17
.
Velocity gradient Velocity/distance [M
0
L
0
T
–1
]
18
.
Pressure gradient Pressure/distance [M L
–2
T
–2
]
19
.
Pressure energy
Pressure × volume
[M L
2
T
–2
]
20
.
Coefficient of
viscosity
Force/area × velocity
gradient
[M L
–1
T
–1
]
21
.
Angle, Angular
displacement
Arc/radius [M
0
L
0
T
0
]
22
.
Trigonometric ratio
(sinθ, cosθ, tanθ, etc).
Length/length [M
0
L
0
T
0
]
23
.
Angular velocity Angle/time [M
0
L
0
T
–1
]
24
.
Angular acceleration Angular velocity/time [M
0
L
0
T
–2
]
25
.
Radius of gyration Distance [M
0
L T
0
]
26
.
Moment of inertia
Mass × (radius of gyration)
2
[M L
2
T
0
]
27
.
Angular momentum
Moment of inertial × angular
velocity
[M L
2
T
–1
]
28
.
Moment of force,
moment of couple
Force × distance
[M L
2
T
–2
]
29
.
Torque Angular momentum/time
Or
Force × distance
[M L
2
T
–2
]
30
.
Angular frequency
2π × Frequency
[M
0
L
0
T
–1
]
31
.
Wavelength Distance [M
0
L T
0
]
32
.
Hubble constant Recession speed/distance [M
0
L
0
T
–1
]
33
.
Intensity of wave (Energy/time)/area [M L
0
T
–3
]
34
.
Radiation pressure
light of Speed
waveofIntensity
[M L
–1
T
–2
]
35
.
Energy density Energy/volume [M L
–1
T
–2
]
36
.
Critical velocity
radiusdensity Mass
viscocityoft coefficiennumber sReynold'
×
×
[M
0
L T
–1
]
37
.
Escape velocity
(2 × acceleration due to
gravity × earth’s radius)
1/2
[M
0
L T
–1
]
38
.
Heat energy, internal
energy
Work (= Force × distance)
[M L
2
T
–2
]
39
.
Kinetic energy
(1/2) mass × (velocity)
2
[M L
2
T
–2
]
40
.
Potential energy
Mass × acceleration due to
gravity × height
41
.
Rotational kinetic
energy
½ × moment of inertia ×
(angular velocity)
2
[M L
2
T
–2
]
42
.
Efficiency
energyor Input work
energyor k output wor
[M
0
L
0
T
0
]
43
.
Angular impulse
Torque × time
[M L
2
T
–1
]
44
.
Gravitational constant
( )
massmass
distanceForce
2
×
×
[M
–1
L
3
T
–2
]
45
.
Planck constant Energy/frequency [M L
2
T
–1
]
46
.
Heat capacity, entropy Heat energy/temperature [M L
2
T
–2
K
–1
]
47
.
Specific heat capacity
etemperaturMass
EnergyHeat
×
[M
0
L
2
T
–2
K
–1
]
48
.
Latent heat Heat energy/mass [M
0
L
2
T
–2
]
49
.
Thermal expansion
coefficient or thermal
expansivity
etemperaturdimension Original
dimensionin change
×
[M
0
L
0
K
–1
]
2
50
.
Thermal conductivity
timeetemperaturArea
thicknessenergyHeat
××
×
[M L T
–3
K
–1
]
51
.
Bulk modulus or
(compressibility)
–1
( )
( )
in volume change
pressurein changevolume ×
[M L
–1
T
–2
]
52
.
Centripetal
acceleration
(Velocity)
2
/ radius [M
0
L T
–2
]
53
.
Stefan constant
[M L
0
T
–3
K
–4
]
54
.
Wien constant
Wavelength × temperature
[M
0
LT
0
K]
55
.
Boltzmann constant Energy/temperature [ML
2
T
–2
K
–1
]
56
.
Universal gas constant
ure temperat mole
volume Pressure
×
×
[ML
2
T
–2
K
–1
mol
–1
]
57
.
Charge
Current × time
[M
0
L
0
TA]
58
.
Current density Current/area [M
0
L
–2
T
0
A]
59
.
Voltage, electric
potential,
electromotive force
Work/charge [ML
2
T
–3
A
–1
]
60
.
Resistance
Current
difference Potential
[ML
2
T
–3
A
–2
]
61
.
Capacitance Charge/potential difference [M
–1
L
–2
T
4
A
2
]
62
.
Electrical resistivity or
(electrical
conductivity)
–1
length
area Resistance ×
[ML
3
T
–3
A
–2
]
63
.
Electric field Electrical force/charge [MLT
–3
A
–1
]
64
.
Electric flux
Electric field × area
[ML
3
T
–3
A
–1
]
65
.
Electric dipole
moment
Torque/electric field [M
0
LTA]
66
.
Electric field strength
or electric intensity
distance
difference Potential
[MLT
–3
A
–1
]
67
.
Magnetic field,
magnetic flux density,
magnetic induction
length Current
Force
×
[ML
0
T
–2
A
–1
]
68
.
Magnetic flux
Magnetic field × area
[ML
2
T
–2
A
–1
]
69
.
Inductance
Current
flux Magnetic
[ML
2
T
–2
A
–2
]
70
.
Magnetic dipole
moment
Torque/magnetic field or
current × area
[M
0
L
2
T
0
A]
71
.
Magnetic field
strength, magnetic
intensity or magnetic
moment density
Volume
moment Magnetic
[M
0
L
–1
T
0
A]
3
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End of Document
209

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FAQs

What are dimensional formulas and why are they important?
Dimensional formulas express physical quantities in terms of fundamental dimensions such as mass, length, and time. They are crucial for checking the consistency of equations in physics and engineering, ensuring that both sides of an equation have the same dimensions. This helps in converting units and understanding how different physical quantities relate to one another. For example, knowing the dimensional formula for force (MLT^-2) aids in deriving other related formulas.

How is the dimensional formula for force derived?
The dimensional formula for force is derived from Newton's second law of motion, which states that force equals mass times acceleration (F = ma). The dimensional formula for mass is [M], and for acceleration, which is the change in velocity over time, it is [LT^-2]. Therefore, combining these gives the dimensional formula for force as [M][LT^-2] = [MLT^-2]. This relationship is fundamental in physics for understanding how forces interact with mass and motion.

What is the significance of dimensional analysis in physics?
Dimensional analysis is a powerful tool in physics that allows scientists and engineers to derive relationships between different physical quantities. By analyzing the dimensions of quantities involved in a problem, one can check the correctness of equations, convert units, and even derive new equations. It simplifies complex problems by reducing them to their fundamental dimensions, making it easier to identify errors and validate results in experimental and theoretical work.

Can dimensional formulas be used for unit conversion?
Yes, dimensional formulas are essential for unit conversion in physics. By expressing quantities in terms of their fundamental dimensions, one can easily convert between different units. For example, if you know the dimensional formula for velocity is [LT^-1], you can convert meters per second to kilometers per hour by using the appropriate conversion factors. This application of dimensional analysis is vital in ensuring accuracy in calculations across various scientific fields.

What are some common physical quantities and their dimensional formulas?
Common physical quantities include area, volume, mass density, force, and energy. For instance, the dimensional formula for area is [L^2], while volume is expressed as [L^3]. Mass density is given by [ML^-3], and energy, which is defined as work done, has the dimensional formula [ML^2T^-2]. Understanding these formulas is crucial for students and professionals in physics and engineering, as they form the basis for more complex concepts.