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Every scientific explanation is explained in terms of a number of physical quantities, each of which expresses a special meaning and importance in context. By definition, a physical quantity is the measurable and quantifiable physical property which has unique information. Based on the directional dependence, physical quantities can be divided into two parts which are scalar and vector quantities. Both scalar and vector quantities are used to determine the movement of an object.
Scalar And Vector Quantities
Scalar Quantity
Scalar quantity is the physical quantity which has only magnitude but do not have direction. Thus, it is a number which is followed by the corresponding unit. Such as, length, mass, speed, etc. have no direction hence they are scalar quantities. The value of the scalar quantity is the same in every direction.
Thus, scalar quantity is a one (1) dimensional parameter which means only magnitude changes when any changes occur in a scalar quantity.
The rules of algebra are applied for combining scalar quantities, such that scalars can be added, subtracted, or multiplied, in the same way, as numbers. But, the operation of scalar quantities with the same measurement unit is possible.
Dot product is the multiplication of two scalar quantities.
Examples of Scalar Quantity
Work
Work is a measure of energy transfer which occurs to or from an object when an applied external force moves the body for a distance. For work to be done, a force must be exerted and also there must be displacement in the force direction. From this we can define work as the scalar product of the force component in the direction of force and the magnitude of force.
Therefore, work done is given as
W=F.D
W = work done
F = force exerted
d = displacement
Speed
The distance travelled by a body in a unit interval of time is termed as speed. Speed is an example of scalar quantity which means the speed has magnitude only. Speed does not have direction.
The speed is given by
Speed=Distance/Time
Unit of speed is given as meter per second which is represented by m/s.
Vector Quantity
Vector quantity is the physical quantity which has magnitude with the specific unit and also a particular direction. Therefore, specifying the direction of action along with its value or magnitude is mandatory while defining or stating a vector quantity. Like, displacement, weight, force, velocity, etc. are vector quantities which have both direction as well as magnitude.
For Vector, Magnitude illustrates the size of quantity, which is also its absolute value, while direction shows the side, that is, East, West, North, South, etc. We express vector quantities in one-dimensional, two-dimensional, or three-dimensional parameters also. Any change in vector size reflects a change in size (magnitude), a change in direction, or a change in both magnitude and direction.
The multiplication of two vector quantities is called as cross product.
When two vectors have the same direction and same magnitude then the vectors are said to be equal.
Examples of vector Quantity
Velocity
Velocity is a Physical Vector Quantity. Velocity has both magnitude and direction also. In calculus, velocity is the first derivative of the displacement with respect to time. Velocity is also defined as the rate of change in the position of an object w.r.t time.
Unit of velocity is given as meter per second which is represented by m/s.
Velocity= Displacement/Time
Velocity=Final Position- Initial Position/Time
Displacement
The displacement is the change in the position of an object with respect to the reference frame. For example, when a car is moving from a house to a grocery store, then its displacement is the relative distance from the grocery store to the frame of reference or the house.
Displacement is given as
Δx=xf-xi
Here,
Δx= displacement
xf= final position
xi= initial position
Acceleration
Acceleration is the rate of change of velocity with time.
Acceleration is given as
Difference Scalar and Vector Quantities
- Scalar quantity has only magnitude. But the vector quantity has both direction and magnitude as well.
- Scalar quantity is one dimensional. But the vector quantity is multidimensional.
- Scalar quantity only changes when magnitude is changed. But the vector quantity changes when magnitude and direction changes.
- Distance, speed are examples of scalar quantity. Whereas displacement and velocity are the examples of vector quantities.
Conclusion
Thus, scalar quantity is a one (1) dimensional parameter.
Length, mass, speed, etc. have no direction hence they are scalar quantities.
Dot product is the multiplication of two scalar quantities.
Work done is given as
W=F.D
The speed is given by
Speed= Distance/Time
Vector quantity is the physical quantity which is multidimensional.
The multiplication of two vector quantities is called as cross product.
Displacement is given as
Δx=xf-xi
Acceleration is given as
