Kinematics Laws of Motion
Table of Contents
- Chapter 1: Introduction to Mechanics
- Displacement, Velocity, and Acceleration
- Chapter 2: Laws of Motion
- Newton’s First Law
- Newton’s Second Law
- Newton’s Third Law
- Chapter 3: Work, Energy, and Power
- Work
- Kinetic Energy
- Potential Energy
- Work-Energy Theorem
- Chapter 4: Gravitation
- Acceleration due to Gravity
- Chapter 5: Oscillations and Waves
- Simple Harmonic Motion (SHM)
- Chapter 6: Thermodynamics
- Zeroth Law
- First Law
- Second Law
- Third Law
- Chapter 7: Electricity and Magnetism
- Ohm’s Law
- Coulomb’s Law
- Magnetic Force on a Moving Charge
- Chapter 8: Modern Physics
- Photoelectric Effect
- Relativity
- Conclusion
- References
Chapter 1: Introduction to Mechanics
Mechanics is the branch of physics that deals with the motion of objects and the forces acting upon them. It is divided into two main branches:
- Kinematics – the description of motion without considering its causes.
- Dynamics – the study of forces and why objects move.
Displacement, Velocity, and Acceleration
- Displacement: A vector quantity that refers to the change in position.
- Velocity: Rate of change of displacement with respect to time.
- Acceleration: Rate of change of velocity with respect to time.
Equation of uniformly accelerated motion are listed below:
(i.) \(v = u + at\)
(ii.) s\(= ut + \tfrac{1}{2}at^2\)
(iii.) \(v^2 – u^2 = 2as\)
Chapter 2: Laws of Motion
Newton’s three laws of motion form the foundation of classical mechanics.
Newton’s First Law
“A body remains at rest, or in uniform motion in a straight line, unless acted upon by a force.”
This is also called the Law of Inertia.
Newton’s Second Law
The acceleration of an object depends on the net force acting upon it and its mass. \(F= ma\)
Newton’s Third Law
“For every action, there is an equal and opposite reaction.”
Example: When you push on a wall, the wall pushes back with equal force.
Chapter 3: Work, Energy, and Power
Work
Work is done when a force is applied on a body and the body is displaced. \(W = F \cdot d \cdot \cos\theta\)
Kinetic Energy
\(K.E. = \tfrac{1}{2}mv^2\)
Potential Energy
\(P.E. = mgh\)
Work-Energy Theorem
\(W_{net} = \Delta KE\)
Chapter 4: Gravitation
Newton’s Law of Gravitation: \(F = G \frac{m_1 m_2}{r^2}\)
Where:
\[G = 6.67 \times 10^{-11} \, Nm^2/kg^2\] is the gravitational constant.
- \(m_1, m_2\) are masses.
- \(r is the distance between them.
Acceleration due to Gravity
\(g = \frac{GM}{R^2}\)
Chapter 5: Oscillations and Waves
Simple Harmonic Motion (SHM)
The restoring force is proportional to displacement: \(F = -k.\)x
Equation of motion: \(x(t) = A \cos(\omega t + \phi)\)
Where:
- A = amplitude
- \(\omega\) = angular frequency
- \(\phi\) = phase constant
Chapter 6: Thermodynamics
Zeroth Law
If two systems are in thermal equilibrium with a third system, then they are in equilibrium with each other.
First Law
\(\Delta U = Q – W\)
Second Law
Heat cannot spontaneously flow from a colder body to a hotter body.
Third Law
As temperature approaches absolute zero, entropy approaches a constant value.
Chapter 7: Electricity and Magnetism
Ohm’s Law
\(V = IR\)
Coulomb’s Law
\(F = k_e \frac{q_1 q_2}{r^2}\)
Magnetic Force on a Moving Charge
\(F = qvB \sin\theta\)
Chapter 8: Modern Physics
Photoelectric Effect
Einstein’s equation: \(E_k = \hbar f – \phi\)
Where:
- \(\hbar f\) = energy of incident photon
- \(\phi\) = work function
- \(E_k\) = kinetic energy of emitted electron
Relativity
\(E = mc^2\)
Conclusion
The conclusion for the whole text will go in this part.
References
List the references here.