Undergraduate
  1. Classical mechanics  1.1. dynamics  1.1.1. Motion in one dimension  1.1.2. Motion in two dimensions  1.1.3. projectile motion  1.1.4. Relative speed  1.1.5. Uniform circular motion  1.1.6. Non-uniform circular motion  1.1.7. Reference frames and transformations  1.2. Newton's Laws of Motion  1.2.1. First law of motion  1.2.2. Second law of motion  1.2.3. Third Law of Motion  1.2.4. Applications of Newton's Laws  1.2.5. Friction and its types  1.2.6. Free Body Diagram  1.2.7. Constraints and pseudo-forces  1.3. Work and Energy  1.3.1. work done by the force  1.3.2. Work–energy theorem  1.3.3. Kinetic energy  1.3.4. Potential energy in classical mechanics  1.3.5. Conservative and non-conservative forces  1.3.6. Energy Conservation  1.3.7. Power and efficiency  1.4. Speed and collisions  1.4.1. Linear momentum  1.4.2. Conservation of momentum  1.4.3. Impulse and impact force  1.4.4. Elastic and inelastic collision  1.4.5. Center of mass and speed  1.4.6. Rocket Propulsion  1.5. Rotational motion  1.5.1. Torque and Angular Momentum  1.5.2. Moment of inertia  1.5.3. Rotational Kinematics  1.5.4. Rotational Energy  1.5.5. Rolling Motion  1.5.6. Precession and gyroscopic motion  1.6. Gravitational force  1.6.1. Newton's law of universal gravitation  1.6.2. Gravitational potential energy  1.6.3. Orbital mechanics  1.6.4. Kepler's laws of planetary motion  1.6.5. Gravitational field and potential  1.7. Fluid mechanics  1.7.1. Pressure and Pascal's Principle  1.7.2. Buoyancy and Archimedes' principle  1.7.3. Fluid Dynamics and Bernoulli's Principle  1.7.4. Viscosity and Poiseuille's law  1.7.5. Surface tension and capillarity  1.8. Oscillations and waves  1.8.1. Simple Harmonic Motion  1.8.2. Damped and driven oscillations  1.8.3. Coupled oscillations and common modes  1.8.4. Wave properties and types  1.8.5. Sound Waves and the Doppler Effect  1.8.6. Wave interference and superposition
  2. Electromagnetism  2.1. Electrostatics  2.1.1. Electric charge and properties  2.1.2. Coulomb's law  2.1.3. Electric field and electric potential  2.1.4. Gauss's Law  2.1.5. Capacitance and Dielectric  2.1.6. Electric dipole and potential energy  2.2. Electric circuits  2.2.1. Current and Resistance  2.2.2. Ohm's law  2.2.3. Kirchhoff's Laws  2.2.4. RC Circuit  2.2.5. AC Circuits and Reactance  2.2.6. Electric power and energy  2.3. Magnetism  2.3.1. Magnetic Fields and Forces  2.3.2. Ampere's Law  2.3.3. Magnetic dipole moment  2.3.4. Biot-Savart law  2.3.5. Magnetic Materials and Hysteresis  2.4. Electromagnetic induction  2.4.1. Faraday's Law  2.4.2. Lenz's law  2.4.3. Self and mutual induction  2.4.4. Transformers and Inductive Circuits  2.5. Maxwell's equations  2.5.1. Gauss's law for electricity  2.5.2. Gauss's law for magnetism  2.5.3. Faraday's law of induction  2.5.4. Ampere-Maxwell law  2.5.5. Electromagnetic waves
  3. Thermodynamics  3.1. Laws of Thermodynamics  3.1.1. Zeroth law of thermodynamics  3.1.2. First law of thermodynamics  3.1.3. Second Law  3.1.4. Third Law  3.2. Heat and work  3.2.1. Heat transfer (conduction, convection, radiation)  3.2.2. Thermal expansion  3.2.3. Heat engines and refrigerators  3.2.4. Carnot cycle and efficiency  3.3. Statistical mechanics  3.3.1. Maxwell–Boltzmann distribution  3.3.2. Entropy and Probability  3.3.3. Partition function  3.3.4. Fermi–Dirac and Bose–Einstein statistics
  4. Optics  4.1. Geometrical Optics  4.1.1. Reflection and Refraction  4.1.2. Mirrors and lenses  4.1.3. Optical Instruments  4.1.4. Fermat's principle  4.2. Wave optics  4.2.1. Interference in wave optics  4.2.2. Diffraction  4.2.3. Polarization  4.2.4. Coherence and holography
  5. Quantum mechanics  5.1. Wave–particle duality  5.1.1. Blackbody radiation in wave–particle duality in quantum mechanics  5.1.2. Photoelectric effect  5.1.3. Compton scattering  5.1.4. De Broglie wavelength  5.2. Schrödinger Equation  5.2.1. Time-independent Schrödinger equation  5.2.2. Particle in a box  5.2.3. Quantum Tunneling  5.2.4. Potential wells and obstacles  5.3. Quantum States  5.3.1. Wave function  5.3.2. Quantum operators  5.3.3. Heisenberg uncertainty principle  5.3.4. Angular momentum and spin
  6. Relativity  6.1. Special relativity  6.1.1. Lorentz transformations  6.1.2. Time expansion and length contraction  6.1.3. Relativistic energy and momentum  6.2. General relativity  6.2.1. Principle of Equivalence  6.2.2. Schwarzschild metric  6.2.3. Gravitational waves  6.2.4. Black holes and event horizons
  7. Solid state physics  7.1. Crystal structure  7.1.1. Bravais lattices  7.1.2. X-ray diffraction  7.1.3. Band theory  7.1.4. Phonons and lattice vibrations  7.2. Electrical and Magnetic Properties  7.2.1. Conductors, Semiconductors and Insulators  7.2.2. Superconductivity  7.2.3. Hall effect
  8. Nuclear and particle physics  8.1. Atomic Structure  8.1.1. Atomic Model  8.1.2. Nuclear binding energy  8.2. Radioactivity  8.2.1. Alpha, beta, gamma decay  8.2.2. Half life  8.2.3. Nuclear Fission and Fusion  8.3. Particle physics  8.3.1. Standard Model  8.3.2. Quarks and Leptons  8.3.3. antimatter  8.3.4. Fundamental interactions
  9. Astrophysics and cosmology  9.1. Stellar evolution  9.1.1. Star formation  9.1.2. Black holes and neutron stars  9.1.3. White dwarfs and supernovae  9.2. Cosmology  9.2.1. The Big Bang Theory  9.2.2. Dark matter and dark energy  9.2.3. Cosmic microwave background

Undergraduate → Classical mechanics → Newton's Laws of Motion ↓


Free Body Diagram


Free body diagrams are an essential tool that physics students learn to use when studying Newton's laws of motion. They provide a simple way to visualize the forces acting on an object, whether that object is a block, an inclined plane, or another body. The beauty of free body diagrams, often abbreviated as FBD, is in their simplicity. They remove all non-essential elements and focus only on the forces at play. This focus helps students and physicists understand how forces interact in the system they are studying.

Understanding free body diagrams

A free body diagram is a graphical illustration used to visualize the forces, movements, and resulting reactions applied to a body in a given situation. The diagram shows the body as a point or a simple shape and uses arrows to represent each force acting on it. The length of the arrow represents the magnitude of the force, while its direction represents the direction of the force. Understanding how to create and interpret these diagrams is important for solving problems involving forces and motion.

Basics of free body diagrams

Let us understand the steps to draw a free body diagram:

  • Identify the object of interest, called the "body" of the free body diagram. This object or body will be different from its surroundings.
  • To focus on the forces applied to the object, replace the object with a simpler representation, often a point or a box.
  • Identify all the forces acting on the object. Each force should be represented by an arrow. According to Newton's third law, the arrows point away from the object if they are applied forces, or toward the object if they are reaction forces.
  • Represents the force of gravity acting downward on the object. It is almost always present, unless otherwise specified.
  • Include all surface forces such as normal force, friction force, tension, applied force, and others, as applicable.
  • According to Newton's third law, any action-reaction force pair acting on the object must be included.

Normal force in free body diagrams

To draw effective free body diagrams, it is necessary to be familiar with the typical forces encountered in mechanics problems. Here are some commonly involved forces:

  • Gravity: A force that pulls objects toward the center of the Earth. Its magnitude is typically calculated by the formula F_g = m * g, where m is the mass of the object and g is the acceleration due to gravity (about 9.8 m/s2 on Earth).
  • Normal Force: The perpendicular contact force exerted by a surface on an object placed on it. It is usually perpendicular to the surface of contact.
  • Friction Force: A force that opposes motion when two surfaces are in contact. It is proportional to the normal force and can be calculated using the formula F_f = μ * F_n, where μ is the coefficient of friction and F_n is the normal force.
  • Tension Force: The pulling force transmitted along the length of a wire, rope, cable, or chain.
  • Applied Force: Any force that is applied to an object by someone or another object.

Example of a simple free body diagram

Consider a box placed on a flat surface with no external forces acting on it other than gravity and the normal force. Here is a simplified free body diagram for this scenario:

    box
    ,
    ,
    | Box |
    ,
    |<--> N |
    ,
    ,
    V
    mg (gravitational force)
N(normal force) mg (gravitational)

More complex free body diagrams: inclined plane

Consider a block sliding down an inclined plane with friction:

The forces to be considered here are gravity, normal force, friction force opposing the motion and any external force if present. Assume the block is moving downwards and let the inclined plane make an angle θ with the horizontal.

    Inclined plane: θ
    Normal force(N)
               ,
              ,
             ,
            ,
           / | Friction force
          / 
         /____→__(block)_____>
        ,
          Gravitational force → sin(θ)
mg sin(θ) N clash

Analysis of free body diagrams

Once the free body diagram is constructed, it can be used to apply Newton's second law of motion: F = m * a. The focus here is on balancing forces in the horizontal and vertical directions in order to find unknowns such as constant force, acceleration, tension, or friction.

Let us consider the example of an inclined plane. The force of gravity can be divided into two components:

  • Perpendicular to the plane: mg * cos(θ)
  • Parallel to the plane: mg * sin(θ)

Force perpendicular to the plane:

  • The normal force N is balanced by the component of gravity perpendicular to the plane: N = mg * cos(θ)

If the block is sliding downwards, then the force parallel to the plane:

  • F_friction + ma = mg * sin(θ)
  • Where F_friction is the friction force opposing the motion: F_friction = μ * N

Practical applications of free body diagrams

Free body diagrams are very useful in various applications ranging from simple mechanics problems to complex engineering challenges. By using FBD effectively, astronomy, civil engineering, biomechanics, automotive engineering, and many other fields solve real-world problems.

Importance in learning physics

Learning how to effectively create and analyze free body diagrams is a vital skill for anyone studying physics. This approach not only improves problem-solving skills but also understanding of how forces interact within a system. Whether dealing with simple static structures or dynamic systems in equilibrium or non-equilibrium, FBD facilitates the visualization of interactions that are otherwise mathematically complex.

Conclusion and final thoughts

Free body diagrams are a powerful visual tool that shows the dynamics of forces acting on a body. They simplify complex problems and form the cornerstone in problem-solving for Newtonian physics. By focusing on these diagrams, students gain a greater appreciation for the dynamics of an object under various forces. This helps to create a path from purely theoretical rules to practical applications.

Mastery of free body diagrams provides students with a baseline ability to tackle increasingly complex physics problems and applications in science and engineering disciplines. Thus, they represent not just a technique, but the mindset needed to understand and express the principles that govern the physical world.


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Free Body Diagram

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