Mechanics

Scalar definition

quantities :

Only magnitude

Distance, speed, mass, temperature

Vector definition

Quantities:

Both magnitude and direction

Displacement, velocity, force/weight, acceleration

(Method to use when adding vectors that are perpendicular)

E.g. Two forces acting perpendicular to each other and have magnitude of 5N and 12N. Find the resultant force, and its direction from the horizontal.

Resultant force : (Pythagoras)

Direction : (trigonometry)

Scale drawings (used when vectors are at an angle)

E.g. A ship travels 30m at a bearing of 060°, then 20m east. Find the magnitude and direction of its displacement from its starting point.

Draw scale diagram, using ruler and a protractor

Resolving vectors

The opposite of adding two vectors, done by using trigonometry.

E.g. A ball has been fired at a velocity of 10m/s, at an angle of 30° from the horizontal, find the vertical and horizontal components of velocity.

X = 10 cos 30º x = 8.7m/s

Y = 10 sin 30° y= 5 m/s

A block of weight 50N is resting on a plane inclined at 15°. Find the vertical and horizontal components of weight acting on the block.