Introduction of Vector & Scalar Quantities

Vector & Scalar Quantities

Scalars are quantities that are fully described by a magnitude only.  For example:

• Time - Scalar quantities often refer to time; the measurement of years, months, weeks, days, hours, minutes, seconds, and even milliseconds.

• Speed and temperature - Two more commonly used scalar quantities in physical calculations are speed and temperature. As long as they did not show any directional movement they will be considered as a scalar quantities. For instance, the measurement of speed in miles or kilometers-per-hour or the measurement of the temperature of the medium both remain scalar quantities as long as they aren’t associated with the direction of the medium’s travel.  

While vectors, are quantities that are fully describe by both magnitude and direction. William Rowan Hamilton (an Irish physicist, astronomer, and mathematician, who made important contributions to classical mechanics, optics, and algebra) has been credited many times for inventing vectors. Vectors must have the same units in order for them to be added or subtracted. For example:

• Force has a value and a direction. You push or pull something with some strength (magnitude) in a particular direction (left or right, north, south, east, or west, or even up or down.)

• weight has a value and a direction. Your weight is proportional to your mass (magnitude) and is always in the direction towards the centre of the earth.

Exercise on differentiating Vector and Scalar Quantities:

1) The football player was running 10 miles an hour towards the end zone.

This is a vector because it represents a magnitude (10 mph) and a direction (towards the end zone). This vector represents the velocity of the football player.

2) The volume of that box at the west side of the building is 14 cubic feet.

This is a scalar. It might be a bit tricky as it gives the location of the box at the west side of the building, but this has nothing to do with the direction of the volume which has a magnitude of 14 cubic feet.

3) The temperature of the room was 15 degrees Celsius.

This is a scalar, there is no direction.

4) The car accelerated north at a rate of 4 meters per second squared.

This is a vector as it has both direction and magnitude. We also know that acceleration is a vector quantity.