Force, Energy and Momentum

• Scalar quantities have magnitude but do not have direction.
• Vector quantities have both magnitude and direction.
• Scalar quantities can be fully described with a number and a unit.
• Vector quantities can be fully described with a number, unit and direction.
• The direction of a vector can be given by:

  1. Bearing
  2. Angle from the horizontal component
  3. Angle from the vertical component
• To add 2 vectors, a scale diagram must be drawn.
• Only 2 vectors can be added using a scale diagram
• Examples of scalar quantities: speed, distance, mass, time, temperature, energy.
• Examples of vector quantities: velocity, displacement, force, acceleration, momentum
• To draw a scale diagram,

  1. Set a scale
  2. Draw the 1st vector
  3. Draw the 2nd vector
  4. Join the tail of the 1st vector to the head of the 2nd vector
  5. Measure the length and direction of the resultant vector
  6. Convert values according to scale
• If vectors are perpendicular:

  (resultant vector)^2 = (Vector 1)^2 + (Vector 2)^2
• 1st Law: An object will remain at rest or in uniform motion in a straight line unless acted upon by an external resultant force
• 2nd Law: The acceleration of an object as produced by the net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.
• F = ma
• F represents resultant force in Newtons (N)
• 'm' represents inertial mass in kilograms (kg)
• 'a' represents acceleration in metres per seconds squared (ms-2)
• 3rd Law: For every action, there is an equal and opposite reaction.
• A moment is defined as the product of force and perpendicular distance from the pivot point to the line of action of the force.
• A moment is also called a torque.
• An object is in equilibrium when:

  There is no resultant force

  There is no turning effect
• Principle of moments: When an object is in equilibrium:

  All anticlockwise moments = All clockwise moments
• Anticlockwise moments are negative
• Clockwise moments are positive
• Moment (Nm) = Force (N) x Perpendicular Distance (m)
• Translation: A single force acting on an object causes a rotation and movement in the direction of the force.
• Couple: 2 equal forces which act on opposite directions but not through the same point so the produce a rotational effect.
• A couple's representation

  
• The line of action is the line that shares the force vectors direction but extends in both directions to infinity.
• If a scale diagram is closed, object is in equilibrium
• If a scale diagram is open, object is not in equilibrium
• The centre of mass of an object is defined as the point at which the entire mass of the object can be considered to be concentrated.
• For a uniform object, the centre of mass is at the centre of the object
• For a non-uniform object, the centre of mass can be found by drawing a perpendicular from the top surface downwards through the centroid (the geometric centre)