mechanics

• the sum of multiple vectors is called the resultant

  the resultant vector is a single vector that has the same effect as all the vectors in play
• scalar = magnitude only
• vector has both magnitude and direction
• the combined effect of three forces on a point is zero, if the resultant of any two forces is equal and opposite to the third
• a moment is the turning effect of a force around a pivot. a pivot is a fixed point around which a body rotates
• moment = force x perpendicular distance from the point to the line of action of the force
• principle of moments: for a system in equilibrium. the sum of the clockwise moments about any point is equal to the sum of the anticlockwise moments about that point
• a couple is a pair of equal and opposite coplanar forces that act to produce rotation
• a couple is a pair of forces that are:

  equal in magnitude

  opposite in direction

  perpendicular to the distance between them
• the moment of a couple is the size of the force multiplied by the perpendicular distance between the two forces
• the centre of mass of an object is the single point at which the entire weight of the object may be considered to act, the weight of the object has no turning effect
• when a suspended object is released or displaced, it will return to an equilibrium position. it comes to rest with the centre of mass directly below the point of suspension
• an object is stable when its centre of mass lies above its base
• displacement is the distance in a given direction
• speed is the change of distance per unit time
• velocity is speed in a given direction
• average speed = distance travelled/time
• Distance-time graphs

  for an object moving at constant speed its graph is a straight line with a constant gradient
• distance-time graphs

  for an object moving at changing speed the gradient changes. the gradient can be found by drawing a tangent
• acceleration = change in velocity per unit time
• a projectile is an object which is falling freely under gravity
• three key principles apply to projectiles

  the motions in the horizontal and vertical planes are independent of one another

  the object will only accelerate in the vertical plane, due to the weight

  as there is no resultant force acting in the horizontal plane, the horizontal velocity of the object will remain constant
• Newtons 1st law

  if the resultant force acting on an object is zero and:

  the object is stationary, remains stationary

  the object is moving, remains moving same speed and direction
• the linear air track can model frictionless motion. the glider on the track glides on a cushion of air. we can compensate for friction by using a tilted runway
• inertia is the tendency of an object to resist a change in motion
• it is harder to change the state of motion of an object having a greater mass (greater inertia)
• Newtons 2nd Law

  for a body whose mass is constant, acceleration is directly proportional to resultant force

  $F=$$ma$
• inertia mass is measured by measuring an objects resistance to changes in velocity, while gravitational mass describes the force of an object in a gravitational field
• terminal speed is when the speed increases and reaches a constant value
• at terminal speed the weight and drag force are balanced (W=D)
• the drag force experienced by an object falling in a fluid will depend on:

  the shape of the object (area of the object facing the fluid)

  speed of the object

  viscosity of the the fluid (how easily the fluid flows past a surface)

  density of the fluid (gas or liquid)
• stopping distance is made up of thinking distance and braking distance
• thinking distance = speed x reaction time

  vto
• braking distance =

  S2= u^2/2a
• stopping distance =

  vto+u^2/2a
• distractions, drugs and alcohol affect the driver reaction times and therefore thinking distance
• braking force, friction, mass/speed of vehicle affect braking distance
• cars have been fitted with various safety features:

  vehicle bumpers, crumple zones, seatbelts, collapsing steering wheel and airbags
• momentum of an object is defined as the product of its mass and its velocity

  $p=$$mv$
• momentum is a vector quantity, the direction of an objects momentum is the same as the direction of the objects velocity