Constants and Fundamental Physical Quantities

Key Physical Constants

Physical constants are values that remain unchanged throughout physics calculations and are essential for solving problems in mechanics, thermodynamics, and waves.

• Acceleration due to gravity (g):

• Universal gravitational constant (G):

• Boltzmann constant (k_B):

Kinematics

Speed, Velocity, and Acceleration

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

• Average speed:

• Average velocity:

• Average velocity (x-component):

• Average acceleration:

• Average acceleration (x-component):

Kinematic Equations (Constant Acceleration)

For motion with constant acceleration, the following equations apply:

Projectile Motion

Projectile motion involves two-dimensional motion under gravity.

• (no horizontal acceleration)

• (vertical acceleration due to gravity)

• (vertical velocity is zero at maximum height)

Vector Components in 2D

Vectors can be broken into components for easier calculation.

• is measured counterclockwise from the x-axis

Relative Motion

Relative motion describes how the velocity of an object changes depending on the observer's frame of reference.

• Where s is the stationary frame, s' is the moving frame, and p is the observed object.

Newton's Laws and Forces

Newton's Laws of Motion

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

• Net force:

• Third law: (action-reaction pairs)

Universal Law of Gravitation

Describes the gravitational force between two masses.

• Near planet surface:

Friction

Friction opposes motion between surfaces.

• Static friction:

• Kinetic friction:

Drag Forces in Fluids

Drag is the resistance force experienced by objects moving through fluids.

• Fast motion:

• Slow motion:

Elasticity

Elasticity describes how materials deform under force.

• Hooke's Law:

• Tensile stress:

• Shear stress:

• Bulk stress:

Circular Motion

Angular and Linear Quantities

Circular motion involves objects moving in a circle at constant or variable speed.

• Angular velocity:

• Linear velocity:

• Centripetal acceleration:

• Centripetal force:

Work, Energy, and Power

Work and Energy

Work is the transfer of energy by a force; energy is the capacity to do work.

• Gravitational potential energy:

• Near planet surface:

• Spring potential energy:

• Work by non-conservative forces:

• If , then

• Power: ; if force is constant and in direction of velocity:

Momentum and Collisions

Linear Momentum

Momentum is the product of mass and velocity; it is conserved in isolated systems.

• If , then

• Impulse:

Center of Mass

The center of mass is the weighted average position of all mass in a system.

Rotational Dynamics

Torque and Rotational Motion

Rotational dynamics deals with the motion of objects rotating about an axis.

• Torque:

• Moment of inertia:

• Rotational kinetic energy:

• Angular momentum:

• If , then

Oscillatory Motion and Waves

Simple Harmonic Motion (SHM)

SHM describes systems where restoring force is proportional to displacement.

• Spring:

• Frequency:

• Pendulum: ;

• Angular frequency:

• Period:

Waves

Waves transfer energy through oscillations.

• Wave speed:

• Transverse wave:

• Wave on string under tension: ;

Standing Waves and Beats

• Fundamental frequency:

• for

• Beats:

Intensity and Sound Waves

Intensity measures the power per unit area; sound waves are longitudinal waves in a medium.

• Sound in liquid:

• Sound in solid:

• Sound in air:

• Decibel level: ;

Spherical Waves and Doppler Effect

• Doppler Effect: (top signs for motion toward each other)

Fluid Statics and Dynamics

Fluid Statics

Fluid statics deals with fluids at rest and the forces they exert.

• ; water at :

• At depth: ;

• Hydraulic press:

• Buoyant force:

• Floating:

• Surface tension:

• Gauge pressure in spherical bubble:

Fluid Dynamics

Fluid dynamics studies fluids in motion.

• Continuity equation: ;

• Bernoulli's equation: along a streamline

Thermodynamics

Thermal Expansion and Ideal Gas Law

Thermodynamics deals with heat, work, and energy transfer.

• Linear expansion:

• Ideal gas law: ;

Heat and Phase Changes

• Phase change (melting/freezing):

• Phase change (vaporization/condensation):

• Change in internal energy:

Work Done by a Gas

• Isobaric process:

• General process:

Summary Table: Key Equations and Constants

Example: To calculate the force of gravity between two masses, use , substituting the values for , , , and .

Additional info: This guide covers the essential equations and constants for introductory college physics, including mechanics, waves, fluids, and thermodynamics. It is suitable for exam preparation and quick reference.