Physics Fundamentals — Study Guide 1
Physics Fundamentals
Study Guide
Intermediate Level • Core Branches of Classical & Modern Physics
This guide walks through the core branches of physics at the intermediate level: classical me-
chanics, rotational motion, oscillations and waves, electromagnetism, thermodynamics, special
relativity, and a brief introduction to quantum mechanics. It assumes single-variable and mul-
tivariable calculus, plus basic linear algebra; vectors are written in bold (F, v). Each section
ends with a practice problem; full step-by-step solutions appear in the final section. Re-derive
each result symbolically before plugging in numbers — the algebra is the lesson.
Contents
1 Classical Mechanics 2
2 Rotational Motion & Angular Momentum 3
3 Oscillations & Waves 3
4 Electromagnetism 5
5 Thermodynamics 6
6 Special Relativity 7
7 Quantum Mechanics Basics 8
8 Solutions to Practice Problems 9
, Physics Fundamentals — Study Guide 2
1. Classical Mechanics
Classical mechanics describes the motion of macroscopic objects at speeds far below the speed
of light. Newton’s three laws are the foundation:
Newton’s First Law (Inertia). A body at rest stays at rest, and a body in motionΣcontinues
in uniform straight-line motion, unless acted on by a net external force. Formally, F = 0 ⇔
dv
dt = 0.
Newton’s Second Law. The net force on a body equals its mass times acceleration, and more
generally equals the rate of change of momentum:
dp
Fnet = ma = , p = mv.
dt
This is a vector equation — components decouple in Cartesian coordinates. Newton’s second
law is the workhorse of mechanics: given forces, integrate to get trajectories.
Newton’s Third Law. For every action there is an equal and opposite reaction: if body A
exerts force FAB on body B, then B exerts —FAB on A. This is the foundation of momentum
conservation for isolated systems.
Work, energy, and the work-energy theorem. The work done by a force along a path is
∫
W = F · dr.
γ
For a constant net force along a straight displacement, W = F d. The kinetic energy K = 12mv2
satisfies Wnet = ∆K — the work-energy theorem.
H
A force is conservative if its work is path-independent, equivalently if F· dr = 0, equivalently
∇×F = 0. Such forces have a potential energy U with F = −∇ U . Gravity and electromagnetism
are conservative; friction is not. For conservative forces, the total mechanical energy E = K + U
is conserved:
dE dK dU
= + = F · v − F · v = 0.
dt dt dt
Momentum conservation. For a system of particles with no external forces, the total mo-
Σ
mentum P = i mivi is conserved. Collisions (elastic or inelastic) are analyzed by combining
momentum conservation with energy conservation (elastic only).
Friction. The static friction force fs ≤µsN prevents motion up to a maximum; once the body
slides, kinetic friction fk = µkN opposes the velocity. Here N is the normal force perpendicular
to the contact surface.
Key formulas: Newton’s second law
Worked mini-example: inclined plane. A block of mass m slides down a frictionless incline
of angle θ. Gravity along the incline is mg sin θ; perpendicular component is mg cos θ balanced
√ √
by the normal. Acceleration a = g sin θ. After sliding distance d, speed v = 2ad = 2gd sin θ.
Energy check: mg(d sin θ) = 21 mv2. Consistent.
Practice Problem 1
A 2 kg block is pushed up a frictionless 30◦ incline with initial speed 5 m/s. How far up the
incline does it travel before stopping? Take g 9.8 m/s2.
Physics Fundamentals
Study Guide
Intermediate Level • Core Branches of Classical & Modern Physics
This guide walks through the core branches of physics at the intermediate level: classical me-
chanics, rotational motion, oscillations and waves, electromagnetism, thermodynamics, special
relativity, and a brief introduction to quantum mechanics. It assumes single-variable and mul-
tivariable calculus, plus basic linear algebra; vectors are written in bold (F, v). Each section
ends with a practice problem; full step-by-step solutions appear in the final section. Re-derive
each result symbolically before plugging in numbers — the algebra is the lesson.
Contents
1 Classical Mechanics 2
2 Rotational Motion & Angular Momentum 3
3 Oscillations & Waves 3
4 Electromagnetism 5
5 Thermodynamics 6
6 Special Relativity 7
7 Quantum Mechanics Basics 8
8 Solutions to Practice Problems 9
, Physics Fundamentals — Study Guide 2
1. Classical Mechanics
Classical mechanics describes the motion of macroscopic objects at speeds far below the speed
of light. Newton’s three laws are the foundation:
Newton’s First Law (Inertia). A body at rest stays at rest, and a body in motionΣcontinues
in uniform straight-line motion, unless acted on by a net external force. Formally, F = 0 ⇔
dv
dt = 0.
Newton’s Second Law. The net force on a body equals its mass times acceleration, and more
generally equals the rate of change of momentum:
dp
Fnet = ma = , p = mv.
dt
This is a vector equation — components decouple in Cartesian coordinates. Newton’s second
law is the workhorse of mechanics: given forces, integrate to get trajectories.
Newton’s Third Law. For every action there is an equal and opposite reaction: if body A
exerts force FAB on body B, then B exerts —FAB on A. This is the foundation of momentum
conservation for isolated systems.
Work, energy, and the work-energy theorem. The work done by a force along a path is
∫
W = F · dr.
γ
For a constant net force along a straight displacement, W = F d. The kinetic energy K = 12mv2
satisfies Wnet = ∆K — the work-energy theorem.
H
A force is conservative if its work is path-independent, equivalently if F· dr = 0, equivalently
∇×F = 0. Such forces have a potential energy U with F = −∇ U . Gravity and electromagnetism
are conservative; friction is not. For conservative forces, the total mechanical energy E = K + U
is conserved:
dE dK dU
= + = F · v − F · v = 0.
dt dt dt
Momentum conservation. For a system of particles with no external forces, the total mo-
Σ
mentum P = i mivi is conserved. Collisions (elastic or inelastic) are analyzed by combining
momentum conservation with energy conservation (elastic only).
Friction. The static friction force fs ≤µsN prevents motion up to a maximum; once the body
slides, kinetic friction fk = µkN opposes the velocity. Here N is the normal force perpendicular
to the contact surface.
Key formulas: Newton’s second law
Worked mini-example: inclined plane. A block of mass m slides down a frictionless incline
of angle θ. Gravity along the incline is mg sin θ; perpendicular component is mg cos θ balanced
√ √
by the normal. Acceleration a = g sin θ. After sliding distance d, speed v = 2ad = 2gd sin θ.
Energy check: mg(d sin θ) = 21 mv2. Consistent.
Practice Problem 1
A 2 kg block is pushed up a frictionless 30◦ incline with initial speed 5 m/s. How far up the
incline does it travel before stopping? Take g 9.8 m/s2.
