1. Mathematics Math in Physics 1 What is a physical quantity? A physical quantity is any quantity that can be measured with a certain mathematical precision. Example: Force What is a dimension? The product or quotient of fundamental physical quantities, raised to the appropriate powers, to form a derived physical quantity. Example: mass x length / time 2 (ML/T 2 ) What is a unit? A precisely defined (standard) value of physical quantity against which any measurements of that quantity can be compared. Example: Newton = kilogram x meters / second 2

2. Mathematics Math in Physics 2 Sytème International length meters (m) time seconds (s) mass kilograms (kg) temperature Kelvin (K) current Amperes (A) amount of substance Mole (mol) luminous intensity candela (cd)

3. Mathematics Math in Physics 3 US Customary System length inches (in, ") time seconds (s) mass pounds (lb) temperature Fahrenheit (F) current Amperes (A) amount of substance Mole (mol) luminous intensity candela (cd)

4. Mathematics Math in Physics 4 Other units length Feet (ft, '), mile (m, mi), furlong, hand time minute (m, min), hour (hr), second (s), fortnight, while force Newton (N) temperature Celsius (C) energy Joule (J) power Watt (W) pressure Pascal (P) magnetic field Tesla (T), Gauss (G)

5. Mathematics Math in Physics 5 Common conversion factors length 1 in = 2.54 cm time 60 s = 1 min, 60 min = 1 hr, 24 hours = 1 day, 365.25 days= 1 yr force 1 N = 0.2248 lb energy 1 J = 10 7 erg, 1 eV = 1.602x10 -19 J power 1 hp = 746 W pressure 1 atm = 101.3 kPa magnetic field 1 T = 10 4 G

6. Mathematics Math in Physics 6 How to convert units

7. Mathematics Math in Physics 7 Most commonly used prefixes for powers of 10 teraT1,000,000,000,00010 12 gigaG1,000,000,00010 9 megaM1,000,00010 6 kilok100010 3 centic0.0110 -2 millim0.00110 -3 microμ0.00000110 -6 nanon0.00000000110 -9

8. Mathematics Math in Physics 8 Common physical quantities Mass Distance Time Speed / Velocity Acceleration Force

9. Mathematics Math in Physics 9 What is scientific notation? 1,562,788.  1.562788x10 6 0.0012789  1.2789x10 -3

10. Mathematics Math in Physics 10 Using scientific notation in calculators When putting numbers in a calculator, it is best to covert them to non-prefixed units first (e.g. 1mm  1x10 -3 m) and then convert back to the desired units when the problem is complete. When using a calculator, it is also better to put in the full number (e.g. 1350x10 -3 m instead of 1.35 m for 1350 mm). In this way you will avoid many of the “decimal place errors” so common in this class.