Physics: Vectors and Scalars Lecture Notes

This set covers fundamental concepts of vectors and scalars, including definitions of vector types, examples of physical quantities, and specific properties of gravitational constants and alloys from medical and university admission test materials.

Null Vector (Zero Vector)

A vector that has zero magnitude, no specific direction, and its initial and terminal points are identical.

Scalar Quantity

A physical quantity that has magnitude only and is not dependent on direction; examples include mass, length, time, temperature, and electric potential.

Vector Quantity

A physical quantity that possesses both magnitude and direction; examples include displacement, velocity, acceleration, force, and weight.

Like Vectors

Two or more vectors of the same type that act in the same direction.

Opposite (Negative) Vector

A vector that has the same magnitude as another vector but acts in the exactly opposite direction.

Unit Vector

A vector whose magnitude is one; it is obtained by dividing a vector by its own magnitude.

Woods Metal

An alloy consisting of $2$ parts Tin, $2$ parts Lead, $4$ parts Bismuth, and $1$ part Cadmium, with a melting point of $60^\circ \text{C}$.

Universal Gravitational Constant ($G$)

A scalar quantity that is a universal constant and does not depend on the mass of the object.

Acceleration due to Gravity ($g$)

A vector quantity that is variable and dependent on location, but is not dependent on the mass of the falling object.

Horizontal Component

The part of a force $F$ acting along the horizontal axis when pulled at an angle $\theta$, calculated as $F\cos(\theta)$.

Vertical Component

The part of a force $F$ acting along the vertical axis when pulled at an angle $\theta$, calculated as $F\sin(\theta)$.

Fundamental Physical Quantities in Mechanics

The basic building blocks of physical measurement in mechanics, specifically Mass, Length, and Time.

Minimum Resultant

The lowest possible value for the sum of two vectors, occurring when they act in opposite directions with an angle of $180^\circ$.

Electric Potential

A scalar quantity defined as the amount of work needed to move a unit charge from a reference point to a specific point inside an electric field.

Electric Intensity (Electric Field)

A vector quantity that describes the force experienced by a unit positive charge placed at a point in an electric field.

Vector Multiplication

The process of multiplying two vectors, which results in either a scalar quantity (dot product) or a vector quantity (cross product).