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The Science of Physics

Discover the essential role mathematics plays in physics, equations, proportional relationships, and dimensional analysis. Learn how to estimate values through order-of-magnitude calculations.

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The Science of Physics

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  1. The Science of Physics The Language of Physics

  2. Mathematics and Physics • Physicists use mathematics to analyze and summarize their observations • Use mathematical relationships among physical quantities to help predict what will happen in new situations • Use tables, graphs, and equations

  3. Mathematics and Physics • Physics equations indicate relationships • Use letters to describe specific quantities • v often stands for velocity or speed • Variables use bold or italics to distinguish them from units which use regular type • Greek letters often describe a mathematical operation • Delta (Δ) means “difference” or “change in” • Subtraction • Sigma (Σ) means “sum” or “total” • Addition

  4. Direct Proportions • Directly proportional – when dividing two sets of quantities by one another gives a constant value • Graphs as a straight line that passes through (0,0) • Can be expressed y x which reads y is proportional to x • y/x=k or y=kx. • When x increases, y increases and vice versa

  5. Inverse Proportions • Inversely proportional – when two sets of quantities have products that are constant • Graphs as a curve called a hyperbola • Can be written as y 1/x which can be read as y is proportional to one divided by x • xy=k • When x increases, y decreases and vice versa

  6. Dimensional Analysis • Treat dimensions like algebraic variables • Can rearrange them in equations by performing the same operation to both sides v = d / t Solve for t

  7. Dimensional Analysis • v = d / t • Multiply both sides by t t * v = d / t * t t’s on the right side cancel out t * v = d

  8. Dimensional Analysis • t * v = d • Divide both sides by v • (1 / v) * t * v = d * (1 / v) • v’s on the left side cancel out • t = d / v • Plug in numbers

  9. Order-of-Magnitude • Gives you a ballpark estimate • Useful if you don’t have a calculator • Use power of 10 closest to actual numbers instead of actual numbers • d = 725km • v = 88km/h • t = ?

  10. Order-of-Magnitude • d = 725km ≈ 1000km • v = 88km/h ≈ 100km/h • t = d / v

  11. Order-of-Magnitude • t ≈ 1000km / 100km/h ≈ 10h • t = 725km / 88km/h = 8.2h

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