physics u1 m1

• Basic physical quantities in Physics

  • Mass (kg)
  • Electric current (A)
  • Length (m)
  • Time (s)
  • Temperature (K)
  • Amount of substance (mole)
  • Luminous intensity (Cd)
• Derived quantity


  Quantities produced by combining basic physical quantities
• Examples of derived quantities

  • Acceleration (m/s^2)
  • Area (m^2)
  • Energy (J)
  • Pressure (Pa)

  
• Scalars


  Physical quantities unaffected by direction, only have magnitude
• Vectors


  Physical quantities that have both magnitude and direction, can be represented on a Cartesian plane

  
• Vector addition


  1. Adding vectors that lie on one plane and act in the same direction

  2. Subtracting vectors that lie on one plane and act in opposite directions

  3. Combining vectors that act at an angle to each other using the parallelogram law

  4. Combining vectors that act at an angle to each other using the triangle law
• Resolving a vector


  1. Determining the horizontal and vertical components of a vector acting at an angle

  2. Using Pythagoras' Theorem to find the resultant vector from the components
• Accuracy


  Proximity of the measured value to the true value, affected by systematic and random errors
• Precision


  Measure of the reproducibility of results, affected by the calibration of the instrument
• Range


  Difference between the maximum and minimum value being measured
• Absolute error


  One half of the smallest unit of measurement
• Relative error


  Ratio of the absolute error to the measurement
• Percentage error


  Relative error multiplied by 100%
• Avogadro's number is 6.022x10^23 molecules per mole
• Homogeneity of equations


  An equation is homogeneous if the base units on the left and right sides are equal
• Dimensional analysis


  Using the dimensions of variables to derive physical equations
• Forces


  • Needed to start, stop, change velocity or direction of motion
  • Not needed to maintain uniform motion due to inertia

  
• Types of motion

  • Linear motion
  • Vertical motion
  • Projectile motion
  • Circular motion

  
• Linear motion terms

  • Distance (scalar)
  • Displacement (vector)
  • Speed (scalar)
  • Velocity (vector)
  • Acceleration (vector)

  
• Equations for linear motion

  1. Acceleration = (final velocity - initial velocity) / time

  2. Average velocity = (initial velocity + final velocity) / 2

  3. Displacement = initial velocity * time + 1/2 * acceleration * time^2

  4. Final velocity^2 = initial velocity^2 + 2 * acceleration * displacement

  
• Newton's Laws of Motion

  • 1st Law: A body at rest stays at rest, a body in motion continues in uniform motion unless acted on by an external force
  • 2nd Law: Resultant force is proportional to rate of change of momentum
  • 3rd Law: For every action, there is an equal and opposite reaction
• Interpreting motion graphs


  1. Displacement-time: Displacement is obtained, gradient is velocity

  2. Velocity-time: Velocity is obtained, gradient is acceleration, area under graph is displacement

  
• Momentum


  Product of mass and velocity, unit is kg m/s
• Principle of conservation of momentum: In a collision, the total momentum before equals the total momentum after
• Proving conservation of momentum for an elastic collision

  Use the principle of conservation of momentum and the fact that kinetic energy is conserved in an elastic collision to derive the relationship between the final velocities of the colliding objects

  
• The graphs below, show displacement time, velocity-time and acceleration time graphs for the same motion

  
• Momentum is defined as the product of mass and velocity of a body
• Momentum


  p = mv, unit = kgm/s
• Principle of Conservation of Momentum


  The total momentum before a collision is equal to the total momentum after the collision
• Elastic collision


  1. Ball of mass m travelling with velocity u collides with ball of mass M at rest

  2. After collision, mass m moves with velocity v and mass M moves with velocity V

  3. 2mV = mu + Mv
• Vertical motion


  Motion of a body that falls on the vertical plane, acted upon by gravity and air resistance
• Free fall


  • Body is only acted upon by the force of gravity, has constant acceleration of 9.81 m/s^2
• When air resistance is considered

  Velocity-time graph is a curve, indicating acceleration is not constant

  
• Terminal velocity


  Final maximum velocity reached when gravitational force is balanced by air resistance
• Equations of motion for vertical motion (neglecting air resistance): v = u - gt, v^2 = u^2 - 2gs, s = ut + 1/2 gt^2

  
• Projectile motion


  Motion of an object acted upon only by the force of gravity, described by a parabolic path

  
• Projectile motion - Horizontal projection

  1. Horizontal velocity is constant, vertical velocity increases due to gravity

  2. Range R = ut, h = -1/2 (g/u)^2 R^2

  
• Projectile motion - Angled projection

  1. Horizontal velocity uh = u cos θ is constant, vertical velocity uv = u sin θ is affected by gravity

  2. Range R = u cos θ * T, h = R tan θ - R^2 (g/2u^2 cos^2 θ)

  
• Circular motion


  Motion of an object rotating about an axis or point, described by a circular path
• Circular motion


  • Tangential/linear speed v = 2πr/T
  • Angular velocity ω = θ/t = dθ/dt, units rad/s
  • Period T = 2π/ω