Physics In Motion And Basic Law

Physics in motion is the study of how objects move and interact with each other. It's a fundamental branch of physics that explores concepts like velocity, acceleration, force, energy, and momentum.

What are the Motions in Physics?

In physics, motion is the change in position of an object concerning its surroundings in a given interval of time. The motion of an object with some mass can be described in terms of the following:

• Distance
• Displacement
• Speed
• Velocity
• Time
• Acceleration

Key Concepts of Physics in Motion:

Velocity: This measures how fast an object is moving and in what direction. It's calculated as distance divided by time.

Acceleration: This measures how quickly an object's velocity changes. It's calculated as the change in velocity divided by the time taken.

Force: A force is a push or pull that can change an object's motion. It's measured in Newtons (N).

Newton's Laws of Motion: These three laws form the foundation of classical mechanics:
First Law: An object at rest stays at rest, and an object in motion stays in motion with constant velocity unless acted upon by an unbalanced force.

Second Law: The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.

Third Law: For every action, there is an equal and opposite reaction.

Energy: Energy is the ability to do work. There are different types of energy, such as kinetic energy (energy of motion) and potential energy (stored energy).

Momentum: Momentum is the product of an object's mass and its velocity. It's a measure of how difficult it is to stop an object.

Examples of Physics in Motion:

A car accelerating:

The force from the engine causes the car to speed up.

A ball falling:

The force of gravity pulls the ball downward, causing it to accelerate.

A pendulum swinging:

The pendulum's motion is governed by the laws of gravity and motion.

A rocket launching:

The force of the rocket engines propels it upward.

Common examples of motion in physics: 

Linear MotionA car accelerating on a highway: The car's position is changing at a constant rate.

A ball falling from a height: The ball's position is changing due to gravity.

Rotational Motion A spinning top:

The top is rotating around its axis.

The Earth revolving around the Sun:

The Earth is rotating around its axis and orbiting the Sun.

Oscillatory Motion A pendulum swinging back and forth:

The pendulum's motion is repetitive.

A vibrating guitar string:

The string oscillates up and down.

Projectile MotionA baseball being thrown: The baseball follows a parabolic path.

A cannonball fired: The cannonball's trajectory is affected by gravity and air resistance.

Circular Motion A satellite orbiting the Earth:

The satellite moves in a circular path.

A car turning a corner:

The car's motion is circular.

Example to illustrate the process:

Problem: A car accelerates from rest to 25 m/s in 5 seconds. What is its acceleration?

Given:Initial velocity (v₀) = 0 m/s
Final velocity (v) = 25 m/s
Time (t) = 5 s

Formula: Acceleration (a) = (v - v₀) / t

Calculation: a = (25 m/s - 0 m/s) / 5 s
a = 5 m/s²

Guide to Unit Conversions

Unit conversion is the process of changing a measurement from one unit to another. It's a fundamental skill in physics, engineering, and many other fields.

Common Units and Their Conversions:

Length:1 meter (m) = 100 centimeters (cm)
1 kilometer (km) = 1000 meters (m)
1 mile (mi) ≈ 1.609 kilometres (km)
1 foot (ft) ≈ 0.3048 meters (m)
1 inch (in) ≈ 2.54 centimeters (cm)

Mass:1 kilogram (kg) = 1000 grams (g)
1 pound (lb) ≈ 0.4536 kilograms (kg)
1 ounce (oz) ≈ 28.35 grams (g)

Time:1 hour (h) = 60 minutes (min)
1 minute (min) = 60 seconds (s)

Temperature:Celsius (C) to Fahrenheit (F): F = (9/5)C + 32
Fahrenheit (F) to Celsius (C): C = (5/9)(F - 32)
Kelvin (K) to Celsius (C): C = K - 273.15
Celsius (C) to Kelvin (K): K = C + 273.15

Force:1 Newton (N) = 1 kg * m/s²

Pressure:1 Pascal (Pa) = 1 N/m²

Conversion Factors and Dimensional Analysis

A conversion factor is a ratio that expresses the equivalence between two different units. For example, 1 mile is equivalent to 1.609 kilometres, so the conversion factor from miles to kilometres is 1.609 km/mi.

Dimensional analysis is a powerful technique for checking the correctness of equations and conversions. It involves ensuring that the units on both sides of an equation are consistent.

Example:Convert 10 miles per hour to meters per second.
Conversion factors: 1 mile ≈ 1.609 km, 1 km = 1000 m, 1 hour = 3600 seconds.
Calculation: 10 mi/h * (1.609 km/mi) * (1000 m/km) * (1 h/3600 s) ≈ 4.47 m/s


Calculating Planetary Motion: Kepler's Laws

Kepler's Laws of Planetary Motion provide a foundational framework for understanding the movement of planets around the Sun. These laws are Law of Elliptical Orbits: Planets orbit the Sun in elliptical paths, with the Sun at one focus.

Law of Equal Areas: A planet sweeps out equal areas in equal times. This means it moves faster when it's closer to the Sun and slower when it's farther away.

Law of Harmonies: The square of a planet's orbital period is proportional to the cube of the semi-major axis of its orbit.


Primary physics principles used in planetary motion are:

Newton's Law of Universal Gravitation: This law states that every particle in the universe attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centres. This law is essential for understanding the gravitational force between the Sun and planets.


Kepler's Laws of Planetary Motion: These laws, derived from observations by Johannes Kepler, describe the motion of planets around the Sun.

Law of Elliptical Orbits: Planets orbit the Sun in elliptical paths, with the Sun at one focus.

Law of Equal Areas: A planet sweeps out equal areas in equal times.

Law of Harmonies: The square of a planet's orbital period is proportional to the cube of the semi-major axis of its orbit.

Conservation of Energy: The total energy of a planet's orbit (kinetic energy + potential energy) remains constant. This means that as a planet gets closer to the Sun (increasing its kinetic energy), its potential energy decreases.

Conservation of Angular Momentum: The angular momentum of a planet remains constant. This means that as a planet gets closer to the Sun, it speeds up to conserve its angular momentum.

These principles, along with other concepts like classical mechanics and celestial mechanics, provide a comprehensive understanding of planetary motion.

Example: Calculating the Orbital Period of a Planet

Given:The semi-major axis of a planet's orbit (a) in astronomical units (AU).
The orbital period of Earth (T_Earth) = 1 year.

Formula:(T_planet / T_Earth)^2 = (a_planet / a_Earth)^3

Example:Let's say we want to find the orbital period of Mars. We know that the semi-major axis of Mars is approximately 1.5 AU.
(T_Mars / 1 year)^2 = (1.5 AU / 1 AU)^3
T_Mars^2 = 3.375
T_Mars ≈ 1.83 years

Therefore, the orbital period of Mars is approximately 1.83 Earth years.

Calculations Velocity: Using Kepler's Second Law, we can calculate the velocity of a planet at any point in its orbit.

Acceleration: The acceleration of a planet is always directed towards the Sun.

Gravitational Force: Using Newton's Law of Universal Gravitation, we can calculate the gravitational force between the Sun and a planet.


Laws of Physics

The laws of physics are fundamental principles that govern the behaviour of the universe. They are based on extensive observation, experimentation, and mathematical reasoning. While there are countless specific laws and principles within physics, some of the most fundamental include:

Classical Mechanics

Newton's Laws of Motion: These three laws form the foundation of classical mechanics and describe the motion of objects.

Law of Conservation of Energy: Energy cannot be created or destroyed, only transferred or transformed.

Law of Conservation of Momentum: The total momentum of a system remains constant unless acted upon by an external force.

Electromagnetism

Coulomb's Law: Describes the force between two electric charges.

Gauss's Law: Relates the electric flux through a closed surface to the enclosed electric charge.

Ampère's Law: Relates the magnetic field around a closed loop to the electric current passing through the loop.

Faraday's Law: Describes the relationship between a changing magnetic field and an induced electric field.

Thermodynamics

Zeroth Law of Thermodynamics: If two systems are in thermal equilibrium with a third system, then they are in thermal equilibrium with each other.

First Law of Thermodynamics: The change in internal energy of a system is equal to the heat added to the system minus the work done by the system.

Second Law of Thermodynamics: The entropy of a closed system always increases over time.

Third Law of Thermodynamics: It is impossible to reach absolute zero temperature.
Relativity

Special Relativity: Describes the laws of physics as seen by observers in relative motion.

General Relativity: Describes gravity as a curvature of spacetime caused by mass and energy.

These are just a few examples of the many laws of physics. Each branch of physics has its own set of laws and principles that govern the behaviour of matter and energy in that particular domain.

Fundamental Formulas

Here are some essential formulas from various branches of physics:

Mechanics:

Force: F = ma (where F is force, m is mass, and a is acceleration)

Work: W = F * d (where W is work, F is force, and d is distance)

Kinetic energy: KE = 1/2 * mv² (where KE is kinetic energy, m is mass, and v is velocity)

Potential energy (gravitational): PE = mgh (where PE is potential energy, m is mass, g is acceleration due to gravity, and h the is height)

Electromagnetism:

Coulomb's law: F = k * q₁q₂ / r² (where F is the electrostatic force, k is Coulomb's constant, q₁ and q₂ are the charges, and r is the distance between them)

Magnetic force on a moving charge: F = q * v × B (where F is the magnetic force, q is the charge, v is the velocity, and B is the magnetic field)

Thermodynamics:

First law of thermodynamics: ΔU = Q - W (where ΔU is the change in internal energy, Q is the heat added, and W is the work done)

Ideal gas law: PV = nRT (where P is pressure, V is volume, n is the number of moles of gas, R is the ideal gas constant, and T is temperature)

Relativity:

Time dilation: t' = t * √(1 - v²/c²) (where t' is the time measured by a moving observer, t is the time measured by a stationary observer, v is the relative velocity, and c is the speed of light)

Length contraction: l' = l * √(1 - v²/c²) (where l' is the length measured by a moving observer, l is the length measured by a stationary observer, v is the relative velocity, and c is the speed of light)