Forces and Newton's Laws

Forces
If a body is in equilibrium (i.e. not accelerating) the external forces acting on it will be balanced.
 * Force is a vector quantity which has both magnitude and direction.
 * Free-body force diagrams show all forces on a single body. All the forces on a free-body force diagram should be shown as arrow labels, showing both size and direction.

Resolving forces:

 * Forces can be resolved in any direction, but to simplify the calculation, forces are usually resolved into two components perpendicular to each other (in 2-dimensional circumstances).

E.g. In this example, W, the weight, is resolved in the direction parallel and perpendicular to the slope. By using trigonometry, the sizes of the two components are Wsinθ and Wcosθ.
 * The size of a component force in a particular direction can be found by using trigonometry.
 * Forces acting at an angle of 90° to its resolving direction, the component parallel to the plane is 0, because cos90° = 0.

Combining forces:
The resultant (total) force can be found by adding the vector components and creating a closed triangle, with the resultant force represented by the third side.

The magnitude of resultant force can be calculated using Pythagorus and the direction can be by using vector addition -- draw the forces as vector arrows 'tip-to-tail'.

Newton's First Law:
'''An object will remain stationary or moving with a constant velocity unless acted on by a net external force. ( ΣF = ma = 0, a = 0)'''

Newton's Second Law:
resultant force (N) = mass (kg) x accelaration (m/s)

Notices:
 * 1) The resultant force is the vector sum of all the forces.
 * 2) The acceleration is always in the same direction as the resultant force and is measured in s/m^2

Newton's Third Law:
If body A exerts a force on body B, then body B exerts the same type of force that is equal in magnitude, but opposite in direction on body A.

Features of paired forces which obey Newton's third law:
-acting on 2 objects

-same magnitude

-opposite directions

-same type of force