1.1.1 SI units:
Time, t seconds, s
Mass, m kilograms, kg
Length, l metres, m
Temperature, t or θ Kelvin, K
Current, I Ampere, A
Amount, n moles, mol
Luminous Intensity, L Candela, cd
These are the base units, all other units can be derived from them. e.g. the Newton – F = ma, (N) = (kg)(ms−2)
1.1.2 Scalars and Vectors
Scalars are de ned as: Quantities with magnitude only.
e.g. mass, speed, time, density
Vectors are de ned as: Quantities with magnitude and direction.
e.g. velocity, acceleration, force, displacement
1.1.3 Vector Addition
Vector addition puts the head of one force to touch the tail of another so that a resultant of the two forces can be found.
1.1.4 Vector Resolution
Vector resolution involves splitting a vector into two co-planar components which are perpendicular to each other (usually vertical and horizontal). Below we can see theforces on an object and then another object on a slope showing those forces resolved parallel and perpendicular to that slope.
1.1.5 Newton’s Laws of Motion
Newton’s First Law:
Every body persists in its state of being at rest or of moving uniformly straight forward, except insofar as it is compelled to change its state by force impressed.
Newton’s Second Law:
The alteration of motion is ever proportional to the motive force impress’d; and is made in the direction of the right line in which that force is impress’d.
Which leads to the formula:
Newton’s Third Law:
To every action there is always an equal and opposite reaction: or the forces of two bodies on each other are always equal and are directed in opposite directions.
1.1.6 Density
Density is de ned as mass per unit volume, with formulae:
1.1.7 Moment of a Force
The moment of a force is de ned as the force multiplied by the perpendicular distance from the pivot, with formulae:
Please note that this is not in the formula booklet.
1.1.8 Principle of Moments
The Principle of Moments states that if an object is balanced, the sum of clockwise moments around a pivot is equal to the sum of anticlockwise moments about the same pivot.
1.1.9 * Torque * All sections labeled with this star are not directly on the syllabus. If there is more than one moment in a system, the resultant moment is known as torque.
1.1.10 Centre of Mass
The centre of mass is where the entire mass of an object appears to be concentrated, and the centre of gravity is the place where the entire weight appears to act, these are often used interchangeably since on Earth, the gravitational eld strength is uniform, so they are in the same place. In order to nd an object’s centre of gravity/mass: On uniform symmetrical objects it is the geometrical centre. On other objects, it can be found by using the fact that an if you support an object at it’s centre of gravity it will always balance, so you attach a plumb-line to it and draw the line down the object after letting it settle, where all the di erent plumb-lines cross must be the centre of gravity.
