Mechanics

• Scalars have size (magnitude) only   vectors have size (magnitude) and direction - can be represented by arrows

• When vectors are added together to find the resultant, we must take account of the direction

• For vectors acting along the same straight line we take one direction as positive and the other as negative

• To add two perpendicular vectors, you can use Pythogoras'  theorem 

• A single vector can be resolved to find its effect in two perpendicular directions

• The component of a vector in any direction is found by mulitplying the vector by the cosine of the angle between the vector and the required direction

• Subtracting a vector is the same as adding a vector of the same size, acting in the opposite direction

• The moment is the turning effect produced by a force

• Moment of a force about a point = force x perpendicular distance from the force to the point

• A couple (or torque) is the effect due to two equal forces acting in the opposite direction

• Couple = magnitude of one force x perpendicular distance between the two forces in the couple

• Principle of moments states: for an object in equilbrium the sum of the clockwise moments about any point = the sum of the anti-clockwise moments about that point

• The centre of gravity of an object is the point at which its entire weight appears to act

• An object will balance if supported at its centre of gravity

• A freely suspended object will always come to rest with its centre of gravity directly below the point of suspension

• Distance and speed are scalar quantities

• Displacement, velocity and acceleration are vectors

• If we can ignore air resistance, all falling objects accelerate downwards at the same rate, know as the acceleration due to gravity, g 

• On Earth, g = 9.81 ms-2

• Terminal velocity is themaximum speed a moving object reaches

• Terminal velocity is caused by air resistance (drag) preventing further acceleration

Newton's First Law - If there is no resultant force acting on an onject

• if it is at rest, it will stay at rest
• if it is moving, it keeps on moving at a constant velocity (at constant speed in a straight line)

Newton's Second Law - The rate of change of momentum of an object is directly proportional to the resultant force acting on it

• the change of momentum takes place in the direction of that force
• if the mass is constant, then force = mass x acceleration

Newton's Third Law - If an object A exerts a force on an object B, then B exerts an equal but opposite force on A

• the inertia of an object is its reluctance to change velocity
• inertia increases with increasing mass

• The momentum, p, of an object depends on its mass, m, and velocity, v     p=mv

• Pricnciple of momentum states: whenever objects interact, their total momentum remains constant, provided that no external force acts on the objects

• Total momentum before the interaction = total momentum after the interaction

• Impulse measures the effect of a force

• Impulse = force x time = change in momentum produced

• The area under a force-time curve gives the total impulse acting, which equals the total change in momentum produced

• Work done = force x displacement in the direction of the force

• Energy is the ability to do work, work and energy are measured in Joules

• Work done = energy transferred

• Power is the rate of doing work                       P = Fv

• The two types of mechanical energy are kinetic energy and potential energy

• Energy is always conserved, though it is not always transferred in useful forms

• If kinetic energy is conserved in a collision, the collision is elastic

• In inelastic collisions, some of the initial kinetic energy is transferred to other forms

• Momentum is always conserved if no resultant external force is acting

• To move an object in a circle there must be a resultant force on it, towards the centre of the circle, called the centripetal force

• An object moving at steady speed in a circle is accelerating because its direction keeps changing, this centripetal acceleration is towards the centre of the circle

• Angles in circular motion are measured in radians

• Angular speed is the angle turned through per second

• Angular speed and linear speed are linked by the equation    v = rw

• Frequency is the number of rotations per second

• Time period is the time taken for one rotation

• All masses attract each other with a gravitational force

• The gravitational field strength g at a point is the force acting on each kilogram of mass in a gravitational field

• g is a vector quantity measured in Nkg-1

• The gravitational potential V at a point is the potential energy of each kilogram of mass in a gravitational field

• V is a scalar quantity measured in Jkg-1 and taken to be zero at infinity

• Change in energy = change in gravitational potential x mass

• All orbital motion is described by Kepler's Laws