Properties of Matter in Physics

Physical quantities can be divided into Fundamental and Derived quantities. Fundamental quantities are independent and form the basis for other quantities. Examples are Mass, Length, and Time. Derived quantities are dependent on fundamental quantities and can be expressed as their combinations. Examples are Speed, Density, and Acceleration.

Speed is the rate of change of distance traveled over time. It is a derived quantity, defined as the ratio of distance to time.

Density is a measure of how much mass is packed into a given volume. It's derived from mass and volume and represents how tightly packed the particles of a substance are.

Acceleration is the rate of change of velocity over time. It is a derived quantity, defined as the ratio of velocity to time. It describes how quickly the speed or direction of motion changes.

The units used to measure physical quantities are standardized in Systems of Units. The most common system is SI (International System of Units). Other systems include CGS and US Customary.

A conversion factor is a ratio that converts one unit of measurement into another. It's used to express the same physical quantity in different units.

Kinetic Energy is the energy of motion, directly proportional to the mass and square of the velocity of an object. It is represented by the formula: 1/2 * m * v^2

Potential Energy is stored energy due to an object's position or state. It is calculated as the product of mass, acceleration due to gravity, and height: m * g * h.

The power of a scientific equation to correctly represent the relationship between physical quantities. It ensures that each term in the equation has the same dimension, allowing for consistent and meaningful calculations.

The total energy possessed by an object due to its motion and position. It includes both kinetic energy (energy due to motion) and potential energy (energy due to position).

The relationship between wavelength (λ) of light, the spacing of slits (d), the order number of interference (n), and the angle of constructive interference (θ) in Young's double-slit experiment. It determines the pattern of light and dark fringes observed on a screen.

The spring constant (K) is a measure of the stiffness of a spring. It relates the applied force (F) to the resulting displacement (x) of the spring.

Dimensional analysis analyzes the physical quantities in an equation by representing them in terms of their fundamental dimensions (e.g., mass (M), length (L), and time (T)).

In dimensional analysis, you find the exponents of the fundamental dimensions (like mass, length, and time) in an equation, ensuring they are consistent on both sides of the equation.

The proportionality symbol (⍺) indicates a relationship where two quantities (e.g., x and a) are related in a way that one changes proportionally to another. For example, x ⍺ a means that x is proportional to a.

In this context, G is the gravitational constant. Its dimensions can be determined by analyzing the dimensions of the other quantities in the equation (F, m1, m2, and r).

Dimension of G: M-1 L3 T-2
This can be derived by ensuring the dimensions of the left side (force, F) and the right side (Gm1m2/r^2) are consistent.

To find the dimensions of G, we need to equate the dimensional expressions of both sides of the equation. By doing so, we can isolate the dimension of G, which is typically expressed as a combination of the fundamental dimensions like mass (M), length (L), and time (T).

Dimensional analysis doesn't give us the exact numerical value of a constant like G. Instead, it helps us understand the relationship between different physical quantities and their units, ensuring the consistency of our equations.

G is the force of gravitation acting between two bodies with masses m1 and m2, separated by a distance r. It's directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

The process of breaking down a physical quantity into its fundamental dimensions: mass (M), length (L), and time (T). This helps analyze the relationship between different physical quantities.

The time it takes for one complete oscillation of a simple pendulum. It depends on the pendulum's length (L) and the acceleration due to gravity (g).

The process of expressing a physical quantity in a different unit of measurement. This is crucial for comparing values in different systems of units.

It's a relationship that connects the quantities involved in a phenomenon, ensuring that both sides of the equation have the same dimensions. It helps validate the correctness of a formula.

A physical quantity that is independent and forms the basis for other quantities. Commonly used fundamental quantities include mass, length, and time.

A physical quantity derived from combinations of fundamental quantities. Examples include speed (length/time), density (mass/volume), and acceleration (velocity/time).