1.2 What are scalar and vector quantities?

A scalar quantity only has magnitude

This is just a numerical quantity (or size), usually with units), but no specific direction.

Examples:

Speed, distance, mass, time, temperature (K or ^oC), potential difference (V), current (A).

Non of these automatically implies the use of direction.

However if you apply a direction to speed or distance, it becomes a vector quantity.

 

A vector quantity has both magnitude (size) and specific direction.

Examples:

Velocity (m/s), is the rate of change of position in a specific direction (compare with speed above)

(you can think of velocity as 'speed in a particular direction', but take care in how you use the words speed and velocity!)

Acceleration (m/s²), is the rate of increase in velocity/speed in a specific direction

Momentum (kg m/s) the product of the mass x velocity of an object moving in a particular direction.

Displacement (m) is the distance an object has moved in a particular direction.

Force (N) is also considered to act in a specific direction.

 

ALL forces are vector quantities

They all have a magnitude, and, at any point, act in a specific direction.

e.g. electrostatic (attraction/repulsion), gravitational, magnetic, (attraction/repulsion) pushing, pulling, tension, compression.

On diagrams vector quantities are usually depicted with an arrow, the length of the arrow can show the magnitude and the angle of the arrow shows the direction along which the quantity acts.

In the diagram above, you have two cyclist travelling at the same speed of 2 m/s, but in opposite directions. Therefore, although they have the same speed (same length of arrow), they have different velocities because they are travelling in different directions. Note that the velocity of the left cyclist is formally given a negative sign to indicate the opposite direction of motion (it doesn't mean going slower or slowing down!).

 

Diagrams illustrating force vectors

Two forces acting on an object.

The length of the arrows are proportional to the magnitude of the forces involved - in this case two acting forces and a resultant force.

One force is acting to the right and the other to the left (blue arrows).

The net force, resultant force, is acting to the right - do you see its a simple logical calculation?

Which is net force to the right = 780 - 330 = 450 N

Lots more on resultant forces on this page and also on Calculating resultant forces using vector diagrams

 

1.   2.     3.  

A parachutist and parachute

These diagrams show the relative magnitude of the two forces acting on a descending parachutist.

Note the relative size and direction of the arrows. The weight force F2 is constant.

1. When the parachutist opens the parachute, there is an immediate large drag force due to big increase in air resistance (air friction).

2. As the parachutist slows down (decelerates) the air resistance (F1) reduces and continues to do so until F1 = F2.

3. When drag force F1 equals the weight force F2 (arrows of equal length), the parachutist is descending at a steady speed - a terminal velocity.

Remember the drag force on an object due to friction (air resistance), increases with speed i.e. as more air brushes over the surface of the object in the same time interval.

 

This parachute situation is fully explained on the Acceleration, friction, drag effects, terminal velocity page