Vectors and Scalars
Vectors and Scalars Overview
- Vectors and scalars are both types of quantities in physics that are expressed as measurements.
- A scalar quantity is only defined by its magnitude.
- A vector quantity is defined by both its magnitude and its direction.
- Examples of scalar quantities include speed, distance, mass, temperature and energy.
- Examples of vector quantities include displacement, velocity, force and acceleration.
Scalars
- A scalar has only magnitude (size).
- Scalars can be added, subtracted, multiplied, and divided like normal numbers, which is termed as scalar arithmetic.
- Examples of scalar quantities: Mass, distance, speed, time, temperature and energy.
- Note that speed is a scalar. It measures the rate of change of distance but disregards the direction of motion.
Vectors
- Vectors have both magnitude and a direction.
- The direction component of a vector separates it from a scalar quantity.
- Vectors are represented by arrows, where the arrowhead points to the direction and the length signifies the magnitude.
- Vector quantities include: Displacement, velocity, acceleration, and force.
- Displacement, velocity, and acceleration are vectors associated with motion.
- It's important to distinguish between velocity (a vector) and speed (a scalar). Velocity includes the speed of an object and its direction of motion.
- Vectors can be added or subtracted — this is a process called vector addition or vector resolution.
Vector Addition
- Vector addition involves geometrical methods to 'add' vectors known as the "head-to-tail" method or parallelogram method.
- If multiple vector quantities are affecting a single body, the resultant vector can be found using vector addition methods.
- Negative vectors: A vector in the opposite direction is considered ‘negative’.
Scalar and Vector Products
- The dot product or scalar product is an algebraic operation that takes two equal-length sequences of numbers and returns a single number.
- The cross product, also known as vector product, outputs a vector which is perpendicular to the vectors being multiplied. The asocioated rules are as per the right-hand rule.
In both the scalar and vector products, consideration must be given to the units used in order to maintain consistency and accuracy.