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Physics: Units, Vectors, and Significant Figures

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  • What must physical quantities have in measurements?
    Physical quantities must have magnitude and units.
  • Why must all units in physics equations be compatible?
    Units must be compatible to ensure equations work correctly; compatible units form a system of units.
  • What is the standard system of units used in physics?
    The Système International (S.I.) system is the standard used in physics.
  • What is a metric prefix?
    A metric prefix is a letter or symbol before a base unit representing a specific power of 10 multiplied by the base unit.
  • How does the number change when shifting from a bigger to a smaller metric unit?
    The number becomes larger when shifting from a bigger to a smaller unit.
  • How does the number change when shifting from a smaller to a bigger metric unit?
    The number becomes smaller when shifting from a smaller to a bigger unit.
  • What is scientific notation used for?
    Scientific notation is used to shorten very long or inconvenient numbers into a more manageable form.
  • How do you convert a number from standard form to scientific notation?
    Move the decimal to get a number β‰₯ 1 but < 10, round to 2 decimals, and use the number of decimal places moved as the exponent.
  • What is the first step in unit conversions?
    Write the given and target units clearly.
  • How do you handle unit conversions with exponents?
    Multiply conversion factors as many times as the exponent indicates.
  • What is dimensional analysis?
    Dimensional analysis checks if the units on both sides of an equation are consistent.
  • What are significant figures?
    Significant figures are the number of digits in a measurement that actually matter for precision.
  • How do you count significant figures in a number with no decimal point?
    Eliminate leading zeros and trailing zeros, then count the remaining digits.
  • What is the rule for significant figures in addition and subtraction?
    Round the answer to the same number of decimal places as the number with the least decimal places.
  • What is the rule for significant figures in multiplication and division?
    Round the answer to the same number of significant figures as the number with the least significant figures.
  • What is the difference between vectors and scalars?
    Vectors have magnitude and direction, while scalars have only magnitude.
  • What is displacement compared to distance?
    Displacement is a vector showing change in position with direction, while distance is a scalar showing total length traveled.
  • How are vectors graphically added?
    Vectors are added by placing them tip-to-tail and drawing the resultant from the start of the first to the end of the last.
  • How do you subtract vectors graphically?
    Subtract by adding the negative of a vector, which has the same magnitude but opposite direction.
  • What happens when you multiply a vector by a scalar?
    The vector's magnitude changes by the scalar, but its direction remains the same.
  • How do you decompose a vector into components?
    Use trigonometry: 𝑨𝒙 = 𝑨 cos(πœ½π’™), π‘¨π’š = 𝑨 sin(πœ½π’™), where πœ½π’™ is the angle with the x-axis.
  • How do you find the magnitude and direction of a vector from components?
    Magnitude: 𝑨 = √(𝑨𝒙² + π‘¨π’šΒ²); Direction: πœ½π’™ = tan⁻¹(π‘¨π’š / 𝑨𝒙).
  • What are unit vectors and their directions?
    Unit vectors have magnitude 1 and point in coordinate directions: π’ŠΜ‚ (x), 𝒋̂ (y), π’ŒΜ‚ (z).
  • How do you add vectors using unit vector notation?
    Add corresponding components: 𝑹⃗ = (𝑨𝒙 + 𝑩𝒙)π’ŠΜ‚ + (π‘¨π’š + π‘©π’š)𝒋̂.
  • How do you describe directions like '30Β° north of east'?
    Draw arrow towards east, then curve 30Β° towards north; use this angle for component calculations.