Vector Calculus
FEW EXAMPLES OF SCALAR QUANTITIES
Quantities with NO direction:
Temperature:
- Temperature is the measure of degree of hotness or coldness of a body.
- It can be measured using thermometer and it can be expressed with a number. $100^{\circ}C$ or $100^{\circ}F$
- Temperature has NO direction.
- Hence it is a SCALAR.
Temperature of a body does not vary based on the object’s position or movementÂ
(i.e.,) We never say, If a body is positioned towards east it will be hotter or if it moves towards south it will be colder.
Time:
- Time is the measure of duration of events.
- Time has NO direction.
- Hence it is a SCALAR.
Mass:
- Mass is the measure of inertia of an object.
- (i.e.) how far it can resist the change in motion when we apply a force on it.
- For example, try to move a metal box and a wooden box, whichever you can move easily has less mass.
- Mass has NO direction.
- Hence it is a SCALAR.
This resistance does not vary based on direction. (i.e.,) If you pull a metal box offers same resistance as if u push the box. That is why we say mass has no direction.
Volume:
- Volume is the amount of space occupied by an object.
- Volume has NO direction.
- Hence it is a SCALAR.
Density:
- Density is the measure of how compact a matter is packed in a volume. $$Density = \frac{Mass}{Volume}$$
- Since mass and volume are scalar, density is also a SCALAR quantity.
Quantities with only ONE direction:
Distance:
- Distance is the total path covered by a vehicle or a person or an object in motion.
- Distance travelled by a vehicle can be measured using an odometer.
- While measuring the distance, we only care about whether the vehicle or person or object moves in forward direction or not. The only direction involved here is FORWARD. Hence distance is an ONE DIMENSIONALÂ problem.Â
- Therefore, distance is a SCALAR quantity.
Speed:
- Speed is the rate at which an object covers a distance.$$speed=\frac{distance}{time}$$
- Since distance and time are scalar, speed is also a SCALAR quantity.
For the question “How much distance travelled??” or “How much speed it is travelling??”…Â
We just need to know whether the vehicle is moving or not (in FORWARD direction). Other things like, ‘it is travelling towards SOUTH-EAST’ or ‘it turned RIGHT’ are not necessary…
Since, Quantities with only one direction can be termed as Scalar, we define distance and speed as scalar.
Quantities with only TWO opposite direction:
Electric Current:
- Electric current is nothing but the rate of flow of electric charges. $$i(t)=\frac{dq}{dt}$$
- In a conductor, large number of randomly moving free electrons present as shown above
- Whenever voltage is applied, electrons inside the conductor gets aligned and begin to flow.