Physics - Mechanics - Vectors

Detailed notes that will help when revising for mechanics

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Chapter 4: Working with vectors
Combining displacements and velocities
In order to calculate displacement trigonometry needs to be used (Pythagoras's theorem may be
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:
Contact force (reaction force)
Air resistance
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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The horizontal velocity will always remain constant
It can worked out using s = ut
The vertical velocity will always increase
It can worked out using the equations of motion
Vectors are quantities that must have a direction associated with them
Vectors can be added if direction is taken into account. Two vectors can be added by means of a
vector triangle. Their resultant can be determined using trigonometry or by scale drawing
Vectors can be resolved into components.…read more


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