Scalar and their Properties
The physical quantities may be broadly classified into the vectors and the scalars. The quantities with magnitude and direction both are known as vector quantities while, the quantities with only magnitude are called scalar quantities.
What is a Scalar Quantity?
Scalar quantities are those quantities which require only the magnitude for their complete specifications. Physical quantities which can be completely specified by a number and unit, and therefore have the magnitude only are scalars. Mass, length, time, energy, volume, density, temperature, electric charge etc. are the examples of Scalar quantity.
Properties of the Scalar Product: Scalar product is a special technique of multiplying two vectors. As the name suggests, we get a scalar quantity after multiplication. Scalar product is also known as dot product (since it is denoted by a dot between the vectors) or inner product.
1. Commutative: The scalar product is commutative, means:
a.b = b.a.
2. Distributive: The scalar product is distributive over addition, means:
a (b + c) = ab + ac.
Time – Scalar Quantities: We often refer Time – Scalar to time, the measurement of years, months, weeks, days, hours, minutes, seconds and milliseconds.
Volume – Scalar Quantity: We can refer Volume – Scalar to the volume of the medium, as in how much of the medium is present. Everything from tons to grams, millilitres and micrograms are all scalar quantities.
Speed and Temperature: Two more commonly used scalar quantities in physical calculations are speed and temperature. As long as they are not associated with a directional movement, they remain scalar quantities. For instance, the measurement of speed in miles or km/hour or the measurement of the temperature of the medium both remain scalar quantities as long as they are not associated with the direction of the mediums travel.