Scalar and Vector Quantities Physics Notes
Scalar Quantities:
The physical quantities, which have magnitude but no direction are called scalars, Mass, length, distance covered, time, density, work, temperature, charge, specific heat, energy, power, speed, length etc. are few examples of scalars, A scalar quantity can be completely described by a number; representing its magnitude. A scalar may be positive or negative. They can be added, subtracted, multiplied and divided according to the simple rules of Algebra.
Vector Quantities:
The Physical quantities which have both magnitude and direction are called vectors. Displacement, velocity, acceleration, force, momentum, electric field, impulse, gravitational field etc. are few exmaples of vector quantities. It may be pointed out that the vectors can not be added, subtracted, multiplied or divided as one may do in case of scalars. It is because, in addition to magnitude, vectors have direction also. Vectors are added, subtracted and multiplied according to the rules of Vector Algebra. The division of a vector by another vector is not a valid operation m Vector Algebra.
1. A physical quantity possesing both magnitude and direction is not necessarily a vector. For example, electric current and pressure. This is; because vectors obey the rules of Vector Algebra and it is possible that a physical quantity which has both mangitude and direction may not obey the vector laws.
2. There are some physical quantities which are neither a scalar nor a vector. These are called Tensor quantities. It does not have one specified direction but have different values in different directions. Examples: Moment of inertia, elasticity constant, stress etc.
Vectors can be divided into two parts:
- Polar vectors
- Axial vectors
1. Polar vectors: Polar vectors are those vectors which have a fixed starting point or a point of application and act along the direction of motion of the body.
For example: Displacement, force etc. are polar vectors.
(a) Polar Vectors
2. Axial vectors: Axial vectors are those vectors which represent rotational effect and act along the axis of rotation in accordance with the “right-hand screw rule”.
For example Angular velocity, angular acceleration, torque, angular momentum, etc. are axial vectors.
(b)
A vector having an anticlockwise rotational ‘ effect, will have its direction along the axis of rotation as shown in figure (b)
Note: Axial vectors describe rotational motion and act along the axis of rotation (according to right-hand screw rule).
Polar vectors describe translatory motion and have fixed starting point. The direction of polar vector remain unchanged irrespective of the coordinate system choosen.