How to Find Dimensional Formula ? Dimensional Formula Trick

Najam Academy
22 May 202308:37
EducationalLearning
32 Likes 10 Comments

TLDRThe video script presents a method for determining the dimensional formulas of various physical quantities. It begins with basic concepts such as velocity, acceleration, and force, using fundamental units like mass (kg), length (meter), time (second), and current (ampere). The script then progresses to more complex formulas for pressure, stress, modulus of elasticity, work-energy, torque, kinetic energy, and electrical concepts like resistance, reactance, and impedance. The method involves combining these fundamental units in a systematic way according to the physical laws that relate these quantities. The script is a valuable resource for those studying physics and engineering, as it simplifies the process of understanding and applying dimensional analysis.

Takeaways
  • 📏 The fundamental physical units are mass (kg), length (meter), time (second), and current (ampere) with their respective dimensional symbols M, L, T, and A.
  • 🏃 The dimensional formula for velocity is derived by using displacement over time, resulting in the formula M^0LT^-1, indicating mass is not a factor.
  • 🚀 For acceleration, the formula is the change in velocity over time, leading to the dimensional formula LT^-2.
  • ⚖️ Force's dimensional formula is derived from mass times acceleration, resulting in the formula MLT^-2.
  • 🔩 Pressure, stress, and modulus of elasticity share the same dimensional formula, which is derived from force over an area (length squared), resulting in the formula [ML^-2T^-2].
  • 💡 Work, energy, torque, and kinetic energy have similar dimensional formulas, all involving mass, length, and time, with specific adjustments for each quantity.
  • 🔌 The dimensional formula for resistance, reactance, and impedance is based on Ohm's law and is given by ML^2T^-3A^-2.
  • 🌡 The dimensional formula for the Boltzmann constant, entropy, and heat capacity involves mass, length squared, time to the power of negative 2, and temperature to the power of negative 1, represented as ML^2T^-2K^-1.
  • 📊 Angular velocity and angular frequency have a simpler dimensional formula, which is M^0L^0T^-1, indicating no mass or length factors.
  • 🎓 Understanding and applying these dimensional formulas is crucial for solving problems in physics and can be beneficial for academic success in exams.
Q & A

  • What is the dimensional formula for velocity?

    -The dimensional formula for velocity is ML^(-1)T^(-1), which indicates that velocity is a measure of distance (length) over time, with mass not being a factor in its dimensions.

  • How is the dimensional formula for acceleration derived?

    -Acceleration's dimensional formula is derived from the definition of acceleration as the change in velocity over time. Since velocity is LT^(-1), the change in velocity (∆V) over time (∆T) gives us the formula L/T^(-2), representing the dimensional symbol for acceleration.

  • What is the relationship between the dimensional formulas of force and acceleration?

    -The dimensional formula for force is derived from the equation force equals mass times acceleration (F = ma). Since the dimensional formula for acceleration is LT^(-2), and the mass (M) has the dimensional symbol M, the formula for force becomes MLT^(-2).

  • How does the script explain the dimensional formula for pressure and stress?

    -Pressure and stress are explained as being equal to force divided by area. The script shows that the dimensional formula for force is ML^(-2)T^(-2), and since area is L^2 (length squared), the L^2 cancels out, leaving the formula for pressure and stress as [M L^(-2) T^(-2)].

  • What is the dimensional formula for work, energy, and the moment of force (torque)?

    -The script explains that work and energy share the same dimensional formula, which is derived from the dot product of force and distance (W = F * d). The formula is ML^2T^(-2). Torque, as the cross product of force and distance, also follows this formula, with the addition of an L factor, resulting in ML^2T^(-2).

  • How is the dimensional formula for kinetic energy calculated?

    -Kinetic energy is calculated as half of the mass times the velocity squared (KE = 0.5 * m * v^2). Using the dimensional symbols, mass is M, and velocity is LT^(-1), the formula for kinetic energy becomes M L^2T^(-2).

  • What is the relationship between voltage, current, and resistance according to Ohm's law?

    -Ohm's law states that voltage (V) is equal to the product of current (I) and resistance (R), or V = IR. The script shows that the dimensional formula for voltage is derived from the formula for work (W = F * d), which gives us ML^2T^(-3)A^(-1), and resistance is the voltage divided by the current, maintaining the same dimensional formula.

  • How does the script describe the dimensional formula for reactance and impedance?

    -Reactance and impedance share the same dimensional formula as resistance, which is derived from Ohm's law and the dimensional formula for voltage. The script shows that this formula is MLS^2T^(-3)A^(-2), indicating that these electrical quantities have the same dimensions.

  • What are the units associated with the dimensional symbols M, L, T, and A?

    -The units associated with the dimensional symbols are as follows: M (mass) is measured in kilograms (kg), L (length) is measured in meters (m), T (time) is measured in seconds (s), and A (current) is measured in amperes (A).

  • How does the script explain the concept of strain being unitless?

    -The script mentions that strain is unitless because it is a ratio of two identical units of length, which cancels out, leaving no units. This is important when considering the dimensional formula for the modulus of elasticity, which is stress divided by strain.

  • What is the significance of noting down these dimensional formulas?

    -The script emphasizes the importance of noting down these dimensional formulas for their utility in solving problems and understanding the relationships between physical quantities. They provide a structured way to approach complex problems and can be crucial for success in exams.

Outlines
00:00
📚 Dimensional Formulas - Basic Concepts and Calculations

This paragraph introduces the method of determining dimensional formulas for various physical quantities. It begins by explaining the fundamental approach to writing down the dimensions of mass (M), length (L), time (T), and current (I), and their respective units (kg, m, s, A). The paragraph then illustrates the process of calculating the dimensional formulas for basic physical quantities like velocity, acceleration, and force by applying the rules of dimensions. The explanation is clear, methodical, and easy to follow, providing a solid foundation for understanding dimensional analysis.

05:02
🔍 Advanced Dimensional Formulas - Pressure, Energy, and More

The second paragraph delves into the application of dimensional formulas for more complex physical concepts. It covers the calculation of pressure, stress, modulus of elasticity, work-energy, torque, and kinetic energy. The explanation is detailed and comprehensive, showing how to relate these quantities to the fundamental dimensions of mass, length, and time. The paragraph also touches on the dimensional formulas for electrical concepts such as resistance, reactance, and impedance, and ends with a note on the formulas for Boltzmann constant, entropy, heat capacity, angular velocity frequency, and angular frequency. The content is rich and provides a thorough understanding of the subject matter.

Mindmap
Keywords
💡Dimensional Formula
A dimensional formula represents the units of measurement for a physical quantity. In the context of the video, it is used to express the relationship between different physical quantities such as mass, length, time, and current. The video demonstrates how to derive the dimensional formulas for various physical concepts like velocity, acceleration, and force by combining these basic units.
💡Velocity
Velocity is a physical quantity that describes the rate of change of an object's position with respect to time. It is calculated as the displacement divided by time. In the video, the process of finding the dimensional formula for velocity involves considering the units of displacement (length) and time, leading to the formula L T^-1.
💡Acceleration
Acceleration is the rate of change of velocity of an object with respect to time. It describes how quickly an object speeds up or slows down. In the video, the process of finding the dimensional formula for acceleration involves considering the change in velocity over time, leading to the formula L T^-2.
💡Force
Force is a physical quantity that describes the interaction between two objects, causing a change in motion. It is calculated by multiplying mass and acceleration. In the video, the process of finding the dimensional formula for force involves using the previously derived formulas for mass and acceleration, resulting in the formula M L T^-2.
💡Pressure
Pressure is the distribution of force applied perpendicular to the surface of an object. It is defined as force per unit area. In the video, the process of finding the dimensional formula for pressure involves using the formula for force and relating it to the units of area (length squared), leading to the formula M L^-2 T^-2.
💡Stress
Stress is a physical quantity that represents the internal forces within a material, responding to an applied load. It is similar to pressure and is calculated as force per unit area. In the video, stress is shown to have the same dimensional formula as pressure, M L^-2 T^-2, because it is essentially a form of pressure.
💡Modulus of Elasticity
The modulus of elasticity, also known as Young's modulus, is a measure of the stiffness of a material. It is defined as the stress required to produce a given strain. In the video, the modulus of elasticity is shown to have the same dimensional formula as stress, M L^-1 T^-2, because strain is unitless and does not affect the dimensions.
💡Work and Energy
Work and energy are related physical quantities that describe the transfer or storage of energy in a system. Work is the product of force and displacement, while energy is the capacity to do work. In the video, the dimensional formula for work and energy is derived by combining the units of mass, length, and time, resulting in the formula M L^2 T^-2.
💡Torque
Torque is a measure of the rotational force acting on an object. It is the product of the force applied and the distance from the pivot point (lever arm). In the video, the dimensional formula for torque is derived by considering the cross product of force and distance, resulting in the formula M L^2 T^-2.
💡Kinetic Energy
Kinetic energy is the energy possessed by an object due to its motion. It is directly proportional to the mass of the object and the square of its velocity. In the video, the process of finding the dimensional formula for kinetic energy involves using the units of mass and the previously derived formula for velocity, leading to the formula M L^2 T^-2.
💡Resistance
Resistance is a property of a material that opposes the flow of electric current. It is defined by Ohm's law as the voltage across a conductor divided by the current through it. In the video, the process of finding the dimensional formula for resistance involves using the previously derived formulas for voltage and current, resulting in the formula M L^2 T^-3 A^-2.
💡Reactance
Reactance is a measure of the opposition to the flow of alternating current (AC) in an electrical circuit, caused by the inductive and capacitive elements in the circuit. It is related to resistance but also depends on the frequency of the AC. In the video, reactance is mentioned as having the same dimensional formula as resistance, M L^2 T^-3 A^-2, due to its relationship with current and voltage.
💡Impedance
Impedance is a term used in AC circuits to describe the total opposition that a circuit presents to the flow of current. It is a complex quantity that includes both resistance and reactance. In the video, impedance is mentioned as having the same dimensional formula as resistance and reactance, M L^2 T^-3 A^-2, due to its role in Ohm's law and its relationship with voltage and current.
Highlights

The introduction of a super easy trick to solve dimensional formula problems.

Explanation of the fundamental units of mass, length, time, and current, and their corresponding dimensional symbols (M, L, T, A).

Derivation of the dimensional formula for velocity using the concept of displacement over time.

The method of shifting terms in the dimensional formula to simplify the expression, as demonstrated with velocity.

The calculation of the dimensional formula for acceleration by relating it to changes in velocity over time.

The derivation of the dimensional formula for force by associating it with mass and acceleration.

The explanation of how pressure and stress are calculated from force and area, leading to the same dimensional formula for both.

The relationship between modulus of elasticity, stress, and strain, and how it leads to the same dimensional formula for these physical quantities.

The process of finding the dimensional formula for work, energy, torque, and kinetic energy, and the similarities in their formulas.

The use of Ohm's law to derive the dimensional formula for resistance, reactance, and impedance.

The calculation of the dimensional formula for voltage by relating it to work, current, and time.

The application of dimensional analysis to derive the formulas for Boltzmann constant, entropy, and heat capacity.

The unique dimensional formula for angular velocity and angular frequency, distinct from other physical quantities.

The emphasis on noting down all the important dimensional formulas for their utility in various exams.

The conclusion that reinforces the learning of the easy trick for solving dimensional formula problems.

Transcripts

Browse More Related Video

UNITS & PHYSICAL QUANTITIES | Physics Animation

SI Base Units and Derived Units - Physics and Chemistry

SI Units Quiz | 40 Questions | International System of Units (SI) | Physics Quiz

Understanding the SI Units (meters, seconds, kg, kelvin, coulomb, candela) MCAT Physics Chemistry

AP Physics 1 review of Torque and Angular momentum | Physics | Khan Academy

Electrical Formulas - Basic Electricity For Beginners

Rate This

5.0 / 5 (0 votes)

Thanks for rating:

Related Tags
Dimensional FormulasPhysics HacksProblem SolvingEducational ContentPhysics ConceptsUnit ConversionAccelerationForceEnergyOhm's Law