Types of scalar physical quantity and vector physical quantity

The physical quantity is any quantity that can be determined and has a unit of measurement in our life, each physical quantity is measured in a special measurement unit, such as the mass, the time, the speed, the energy, and the velocity.

Physical quantities

The physical quantity is divided into the scalar physical quantity and the vector physical quantity. The scalar physical quantity is the physical quantity that has magnitude only and has no direction, to describe the scalar physical quantity, It is enough to know its magnitude only by giving its numeric and its measuring unit, such as we say the body mass equals 10 kilograms.

The length and time are scalar physical quantities because they have magnitude only and have no direction. All the scalars are subject to the algebraic mathematical operations related to the numbers and especially they are added and subtracted if they have the same measurement units.

The vector physical quantity is the physical quantity that has the magnitude and the direction, to describe the vector physical quantity, It is necessary to know its magnitude (its numeric value and measuring unit) and also its direction. The acceleration and the force are the vector quantities because they have the magnitude and direction.

All the vectors are subject to the mathematical operations called vectors algebra, The vectors have great importance in different fields of physics and applied science like engineering. Understanding various physical phenomena such as gravity, the movement of liquids and the geometrical establishments depends basically on the main properties of vectors.

Distance and displacement

The displacement is the length of the shortest straight line between two positions (the primary position and the final position), It is determined by the magnitude and the direction, It is a vector quantity, It is measured by meter or kilometer.

The distance is the actual length of the path that a moving object covers from the start point to the endpoint, It is determined by magnitude only, It is a scalar quantity, It is measured by meter or kilometer.

The displacement equals the distance (numerically) when the object moves in a direct straight line in one direction, The two equal displacements have the same magnitude and the same direction.

The direction is determined from the starting point of the movement towards the final point, The displacement equals zero when the start point is the endpoint.

The velocity and speed

The velocity is the rate of change of displacement, or it is the displacement covered in one second (unit time), The velocity is a vector quantity, and to determine it accurately, It is necessary to identify its magnitude and direction.

The predator (Cheetah) is one of the fastest wild animals, its speed is about 27 m/s, but if we want to represent its velocity, we say that its velocity is 27 m/s in a certain direction, we say that the cheetah’s velocity equals 27 m/s in the west direction.

The velocity is the speed in a given direction when the body moves in a straight line in one direction, The velocity is measured by meter/second or kilometer /hour.

The speed is the distance covered in a unit of time, It is determined by a magnitude only, It is a scalar quantity, and it is measured by meter/second or kilometer /hour.

The acceleration

The acceleration is the change of an object’s speed in one second, we use the acceleration unit (m/s²) when the distance is measured in meters and the time is measured in seconds or (km/h²) when the distance is measured in kilometers and the time is measured in hours.

When a car covers equal distances at equal periods, It is said that the object moves with uniform speed but its speed changes (decreasing or increasing) by equal values at equal periods, it is said that it moves by uniform (regular) acceleration.

Uniform acceleration is the change (increase or decrease) of the object’s speed by equal values through equal periods.

When the car’s speed increases over time (its initial speed < its final speed), the movement is described as the accelerating motion or positive acceleration.

When the car’s speed decreases over time (its initial speed > its final speed), the movement is described as decelerating motion or negative acceleration.

Types of physical quantities

Physical quantities are either fundamental (such as mass or length) or derived from these fundamental quantities (such as velocity or force). They can also be categorized as scalars or vectors depending on their directional properties. Physical quantities are properties or characteristics of phenomena, objects, or systems that can be measured.

Fundamental (Base) Quantities

• Length (L): Measured in meters (m).
• Mass (M): Measured in kilograms (kg).
• Time (T): Measured in seconds (s).
• Electric current (I): Measured in amperes (A).
• Temperature (Θ): Measured in kelvins (K).
• The amount of substance (N): Measured in moles (mol).
• Luminous intensity (J): Measured in candelas (cd).

Derived Quantities

Derived quantities are those that are derived from the fundamental quantities by combining them through mathematical relationships. Examples of derived quantities include:

• Area (A): Measured in square meters (m²). Derived from length.
• Volume (V): Measured in cubic meters (m³). Derived from length.
• Velocity (v): Measured in meters per second (m/s). Derived from length and time.
• The acceleration (a) is measured in meters per second squared (m/s²), and it is derived from velocity and time.
• Force (F): Measured in newtons (N). Derived from mass, acceleration (F = ma).
• Energy (E): Measured in joules (J). Derived from force and distance.
• Power (P): Measured in watts (W). Derived from energy and time.
• Pressure (P): Measured in pascals (Pa). Derived from force and area.
• Electric charge (Q): Measured in coulombs (C). Derived from current and time.
• Electric potential (V): Measured in volts (V). Derived from energy and charge.
• Frequency (f): Measured in hertz (Hz). Derived from time.

Scalar and Vector Quantities

Physical quantities can also be classified as scalars or vectors based on whether they have direction:

• Scalar Quantities have magnitude but no direction, such as Mass, temperature, speed, energy, distance, and time.
• Vector Quantities have both magnitude and direction, such as Force, velocity, acceleration, displacement, and electric field.

Dimensional and Non-Dimensional Quantities

• Dimensional Quantities: These have physical dimensions (e.g., length, mass, time). Examples: Velocity [LT⁻¹], Force [MLT⁻²].
• Non-Dimensional Quantities are pure numbers without physical dimensions. Examples: Refractive index, coefficient of friction, strain.

Static objects, Moving objects, Types of Motion and Velocity

Uniform Acceleration and Non-uniform Acceleration

Safety skills, Applications of motion with uniform acceleration (Freefall & Projectiles)

Scalar Quantities, Vector Quantities & Finding the resultant of two perpendicular forces

Types of speed & Factors necessary for the description of motion