Fundamental Constants and Physical Quantities

Important Physical Constants

Physical constants are essential for calculations in physics, providing fixed values for universal properties.

• Acceleration due to gravity (g): 9.80 m/s2

• Gravitational constant (G): 6.67 × 10-11 Nm2/kg2

• Elementary charge (e): 1.60 × 10-19 C

• Coulomb's constant (k):

• Permittivity of free space (\(\varepsilon_0\)): 8.85 × 10-12 F/m

• Speed of light (c): 3.00 × 108 m/s

• Electron mass (me): 9.11 × 10-31 kg

• Proton mass (mp): 1.67 × 10-27 kg

Integral Table

Common Integrals Used in Physics

Integrals are frequently used to solve problems involving motion, fields, and energy.

• , for

Mechanics: Kinematics and Dynamics

Kinematics Relations

Kinematics describes the motion of objects without considering the forces causing the motion.

• Velocity:

• Displacement:

• Acceleration:

• Change in velocity:

• Position (constant acceleration):

• Velocity (constant acceleration):

• Velocity squared:

Rotational Kinematics

Rotational motion is described using angular quantities analogous to linear motion.

• Angle:

• Angular velocity:

• Angular acceleration:

• Centripetal acceleration:

Newton's Laws and Forces

Newton's laws govern the relationship between forces and motion.

• Newton's Second Law:

• Newton's Third Law:

• Gravitational force:

• Friction (kinetic):

• Friction (static):

• Spring force:

• Universal gravitation:

Energy, Work, and Power

Work and Energy Relations

Work and energy are fundamental concepts describing the ability to cause change.

• Work:

• Work (constant force):

• Power:

• Power (force and velocity):

• Kinetic energy:

• Potential energy (gravitational):

• Potential energy (spring):

• Change in energy:

• Change in thermal energy:

• Force from potential energy:

Momentum and Impulse

Linear Momentum and Impulse

Momentum is a measure of motion, and impulse is the change in momentum due to a force.

• Momentum:

• Impulse:

• Impulse (constant force):

• Force and momentum:

Rotation and Oscillations

Torque and Rotational Inertia

Torque causes rotational motion, and rotational inertia quantifies resistance to rotation.

• Torque:

• Torque (vector):

• Torque (magnitude):

• Moment of inertia (discrete):

• Moment of inertia (continuous):

Simple Harmonic Motion

Oscillatory motion is described by sinusoidal functions.

• Position:

• Velocity:

• Acceleration:

• Energy:

• Angular frequency:

Vectors and Vector Operations

Dot and Cross Product

Vectors are fundamental in physics, and their operations are used to describe physical quantities.

• Dot product:

• Cross product (magnitude):

• Cross product (components):

Trigonometric and Approximation Relations

Trigonometric identities and approximations are useful for simplifying expressions.

• (for small \(\theta\))

• (for small \(x\))

• (for small \(x\))

• (for small \(x\))

Electrostatics: Electric Forces and Fields

Electric Force and Field Equations

Electrostatics deals with forces and fields due to electric charges.

• Force on a charge:

• Coulomb's Law:

• Electric field (point charge):

• Electric field (line charge):

• Electric field (surface charge):

• Electric field (volume charge):

Gauss's Law and Electric Flux

Gauss's Law relates the electric flux through a surface to the charge enclosed.

• Electric flux:

• Gauss's Law:

Symmetry and Dipoles

Symmetry simplifies calculations of electric fields for certain charge distributions.

• Use symmetry for: Spherical and cylindrical charge distributions

• Electric dipole moment: points from negative to positive,

• Field along axis of dipole:

• Field perpendicular to dipole:

Examples and Applications

• Example (Electric Field): The electric field at a distance from a point charge is .

• Example (Work): The work done by a constant force over a displacement is .

• Example (Impulse): A force applied for a time changes momentum by .

Summary Table: Key Equations

Additional info: Academic context and explanations have been added to clarify the meaning and application of each equation and concept, making the notes suitable for exam preparation and self-study.