# Physics - Mechanics - Vectors

Detailed notes that will help when revising for mechanics

- Created by: George Beresford
- Created on: 13-03-12 11:18

First 351 words of the document:

Chapter 4: Working with vectors

Combining displacements and velocities

In order to calculate displacement trigonometry needs to be used (Pythagoras's theorem may be

used)

Always state the magnitude of the displacement and the angle the displacement makes with the

positive x axis

If you are travelling at an angle then we can break down the resultant velocity into its horizontal and

vertical components

Likewise if we wanted to work out the resultant velocity we could used trigonometry to work it out

Combining forces

Several forces usually act on a body:

Weight

Contact force (reaction force)

Air resistance

Friction

If we know all of the forces we can work out the resultants and then work out the acceleration using

Newton's laws of motion

If the forces are acting in the same direction (+/-) then it's a simple subtraction or addition to find

the resultant

If the forces are acting at right angles to each other then we use Pythagoras's theorem and basic

trigonometry to work out the angle at which the resultant force is acting

When there is more than 3 forces we can create a shape of forces (depending on how many forces

are acting)

If an object is in equilibrium, the forces acting on it must add up to zero

Components of vectors

If we have a force F acting at an angle x to the horizontal we can work out the horizontal and

vertical components

Fy = Fsin(x)

Fx = Fcos(x)

Understanding projectiles

A projectile is an object which is given an initial push and which then moves freely through the air

Make sure to use a consistent sign convention

Write down what you know

Write down what you are trying to find

Find the most suitable equation of motion

Substitute numbers in

A curved trajectory simply requires components of the velocities to be worked out

Projected horizontally

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