Scalar and vector quantity

Scalar and vector quantity

Scalar and vector quantity – The physical quantities are of two types: Scalars and Vectors.

A Scalar quantity

A physical quantity which has only magnitude and no direction is called a scalar quantity or scalar. The scalars can be added, subtracted, multiplied and divided by ordinary law of algebra. Mass, length, time, distance, speed, temperature, work etc. are a few examples of scalars.

A Vector quantity

A physical quantity which has magnitude as well as direction is called a vector quantity or vector. Velocity, force, weight, momentum, impulse, torque, temperature gradient, gravitational field etc. are the some of the examples of vector. Vectors cannot be added, subtracted, multiplied by ordinary law of algebra. For these operations on vectors we have to use laws of vectors. It is important to note that the division of a vector by another vector is not defined because the division of a vector by a direction is not possible.

Calculating vector quantity

It is worth mentioning here that if a particle is subjected to two velocities simultaneously its resultant velocity is different from the two velocities and is obtained by using a special rule. Suppose a particle is moving inside a long tube with speed of 6 m/s and tube itself is moving in the room at speed of 8 m/s along a direction perpendicular to its length. The following figure represents the position of the tube and the particle at initial instant and after a time interval of 1 sec. Geometrical analysis gives the result that ball has moved a distance of 10 m in a direction θ = 53⁰ from the tube. Hence the resultant velocity of the ball is 10 m/s along this direction.

vector-quantity
Resultant of vector-quantity

Vectors can be broadly divided in two types :

 Polar vectors

These are those vectors which have a starting point or a point of application. For example, displacement force, etc., are polar vectors.

polar- vectors
polar- vectors

Axial vectors

These are those vectors which represent rotational effect acts alone the axis of rotation in accordance with right hand screw rule. For example, angular velocity, torque, angular momentum etc., are axial vectors. For a vector having anticlockwise or clockwise rational effect, It will have its direction along the axis of rotation as shown in following figure.

Axial vectors
Axial vectors