physics

• Base quantities and SI units


  • mass (kg)
  • length (m)
  • time (s)
  • current (A)
  • temperature (K)
  • quantity of matter (mol)
• Derived quantities


  Physical quantities other than the basic quantities, obtained from a relation between derived quantities and other basic quantities
• Dimensions


  Useful to relate the physical quantity to the basic quantities, denoted by M (mass), L (length), T (time), A (electric current), Θ (temperature), N (quantity of matter)
• Dimensional analysis


  1. Checking the homogeneity of an equation

  2. Constructing empirical equations
• Addition and subtraction can only be done on physical quantities with the same dimensions
• Every term of an equation must have the same dimension
• Left and right side of an equation must have the same dimension
• Equations using dimensional analysis


  • v = ut + 1/2 at^2
  • s = ut + 1/2 at^2
  • c = √(T/ρ)
• Scalar quantity


  Physical quantity with only magnitude
• Vector quantity


  Physical quantity with both magnitude and direction
• Operations with vectors


  1. Sum of vectors (parallelogram, triangle, polygon)

  2. Resolving a vector into perpendicular components

  3. Multiplication of vector with a scalar

  4. Vector product (dot product, cross product)
• Scalar quantities


  • kinetic energy
  • work
  • speed
• Vector quantities

  • displacement
  • force
  • velocity
  • momentum
  • acceleration
• A plane flies 120 km north then 50 km east


  Resultant displacement is 130 km at 22°37' from north
• Determining vector r in terms of vectors a and b

  r = a + b

  ii. r = a - b

  iii. r = a - b

  iv. r = -a - b
• A plane flies 120 km to the north then 50 km to the east
• Resultant displacement

  120a + 50b = 130 km
• tan θ = 50/120


  θ = 22°37' from North or 67°23' from positive r-axis
• Four coplanar forces lying on the r-n plane act on a particle
• Resultant force


  30.7 N at 208° from positive r-axis
• Three horizontal forces act on a particle

  
• Resultant force


  10.8 N at 68.2° from positive r-axis
• Change in velocity


  4.2 m/s at 45° from positive r-axis
• Measurement has errors or uncertainty
• Absolute error


  Represents the error in a measurement
• Fractional error


  Absolute error divided by the measured value
• Percentage error

  Fractional error multiplied by 100
• Types of errors

  • Systematic errors
  • Random errors
• Systematic errors


  Zero errors, instrumental error, incorrect assumption, observer error, magnitude of error is constant
• Random errors

  Parallax errors, magnitude of error is not constant
• Plastic tube external diameter L = (54 ± 2) mm, internal diameter X = (37 ± 1) mm
• Maximum absolute error for L - X

  3 mm
• Maximum percentage error for L - X


  18%
• Maximum absolute error for (L - X)/X

  1.1 mm
• Maximum percentage error for (L - X)/X


  6.5%
• Steel ball bearing density has 2% mass error and 3% diameter error
• Maximum percentage error in density


  11%
• Methods to reduce random errors with micrometer screw gauge

  • Take repeated readings
  • Have someone else take the measurements
• Parallax errors


  Random errors caused by the observer's line of sight not being perpendicular to the scale being read
• Parallax errors are random errors, not systematic errors