Essential Physics Formulas for Mechanics

Posted on Jun 28, 2025 in Physics

Kinematics: Motion Equations

Equation of Position

  • Xf = Xi + Vit + at2/2
  • Xf = at2/2 (when Xi and Vi are zero)

Equation of Velocity

  • Vf = Vi + at
  • Vf = at (when Vi is zero)
  • Vi = -at (rearranged)

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Acceleration Formulas

  • a = (Vf – Vi) / (tf – ti) (Average Acceleration)
  • a = 2Xf / t2 (when Xi and Vi are zero)
  • a = -Vi / t (rearranged)
  • a = F / m (from Newton’s Second Law)

Time Calculations

  • t = -Vi / a (rearranged)

Related Concepts & Formulas

  • Average Velocity: V = (Xf – Xi) / (tf – ti)
  • Newton’s Second Law: F = m * a

Note: The following formulas (A=b*h, X=b*h/2, a=Vf/t) might be context-dependent, possibly related to graphical analysis of motion.

  • A = b * h (Area, e.g., under a velocity-time graph for displacement)
  • X = b * h / 2 (Area of a triangle, e.g., under a velocity-time graph for displacement)
  • a = Vf / t (Acceleration, when Vi is zero)


Vertical Motion & Free Fall Equations

For objects in free fall near Earth’s surface:

  • Yf = 0 (when the object reaches the ground)
  • Vi = 0 (if the object starts from rest)
  • a = -9.8 m/s2 (acceleration due to gravity, assuming upward is positive)

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Free Fall Formulas

  • 0 = Yi + Vit + (1/2)at2 (General position equation, Yf=0)
  • 0 = Yi + (1/2)at2 (when Vi=0)
  • Yi = -(1/2)at2 (rearranged from above)
  • t = √(-2Yi / a) (Time to reach ground, when Vi=0)


Circular Motion: Key Definitions

Radian
An angle formed at the center of a circle by an arc whose length is equal to the radius.
Angular Velocity (ω)
Obtained by dividing the angular displacement by the time taken to travel that displacement.
Tangential Velocity (vt)
The magnitude of velocity that maintains a trajectory perpendicular to the radius of the circumference when an object moves in a circular path.
Frequency (f)
The number of cycles per unit of time that a body performs in circular motion.
Period (T)
The time it takes for an object in circular motion to complete one full revolution.
Centripetal Acceleration (ac)
The magnitude that causes circular motion and points directly towards the center of rotation.
Centripetal Force (Fc)
The magnitude that is directed towards the center of the circumference, meaning “center-seeking.”
Torque (τ)
Occurs when a force is applied to produce a twisting or rotational effect on an object.


Circular Motion: Essential Formulas

  • 1 Radian ≈ 57.3 degrees
  • θ = angle in radians
  • θ = s / r (Angular displacement, where s is arc length, r is radius)
  • s = θ * R (Arc length)
  • ω = 2πf (Angular velocity from frequency)
  • ω = θ / t (Angular velocity from angular displacement and time)
  • v = rω (Tangential velocity)
  • at = rω2 (Tangential acceleration)
  • ac = v2 / r (Centripetal acceleration)
  • Fc = m * ac (Centripetal force)
  • τ = F * r (Torque, when force is perpendicular to radius, i.e., angle = 90°)
  • τ = F * r * sin(θ) (Torque, when the angle θ between force and radius is different from 90°)


Forces & Equilibrium: Fundamental Concepts

Friction
A natural resistance to sliding motion between materials in contact or within a medium, acting parallel to the surfaces.
Free Body Diagram
A representation, in a coordinate system, of all the forces acting on a body in specific situations.
Normal Force (FN)
The force exerted by a surface on a body that is sliding or at rest on it, acting perpendicular to the surface.
Statics
The branch of Mechanics responsible for analyzing the equilibrium of bodies.
Coefficient of Friction (μ)
The constant of proportionality characteristic of the materials that are in contact.
Equilibrant Force
A force applied with the same magnitude and direction, but in the opposite sense to the resultant force, to achieve equilibrium.
Concurrent Forces
Two or more forces that act at the same point.
Coplanar Forces
Two or more forces that lie in the same plane.
Non-Coplanar Forces
Two or more forces that exist in a three-dimensional space and do not lie in the same plane.
Non-Concurrent Forces
Two or more forces that do not act at the same point.
Dynamics
The branch of Mechanics that studies the causes of motion and changes in motion.


Forces & Equilibrium: Calculation Formulas

  • FA = m * a (Applied Force from Newton’s Second Law)
  • a = FA / m (Acceleration from Applied Force)
  • w = m * g (Weight)
  • m = w / g (Mass from Weight)
  • FAx = FA * cos(θ) (X-component of Applied Force)
  • FAy = FA * sin(θ) (Y-component of Applied Force)
  • f = μ * FN (Friction Force, where μ is the coefficient of friction)
  • Tx = T * cos(θ) (X-component of Tension)
  • Ty = T * sin(θ) (Y-component of Tension)
  • FN + FAy – w = 0 (Equilibrium in Y-direction, if FAy is upward)
  • FN = w – FAy (Normal Force, rearranged)
  • F – Tx = 0 (Equilibrium in X-direction, example)
  • Ty – w = 0 (Equilibrium in Y-direction, example)