Dimensions of Some Common Physical Quantities

Dimensions of Some Common Physical Quantities • How to interpret this: Ex: a = x t2 So, which of the following quantities have dimensions of acceleration? • a = xt2 b) a = v2/x c) a = x/t2d) a = v/t ANSWER: b & d

Equations • EQUATION- a mathematical expression that relates physical quantities • Physical quantity- property of a physical system that can be measured, like length, speed, acceleration, or time duration. • Used to express/way of thinking about fundamental ideas • Can be rearranged to give information about any physical quantity in it • v = (d / t) can be re-written as d = (v × t) or t = (d / v)

Measured & Calculated Values • Measurements require accuracy and precision • ACCURACY- a measure of how close the measured value of a quantity is to the actual value • PRECISION- a measure of how close together the values of a series of measurements are to one another

Significant Figures • SIGNIFICANT FIGURE- the digits actually measured plus one estimated digit in a properly expressed measurement • Measurements are ALWAYS reported in sig-figs • The more sig-figs in a measurement, the more accurate it is. Significant numbers in a measurement: • All non-zeros • 0.743  3 sig-figs • 44.98  4 sig-figs • 0s appearing between non-0 digits or significant zeros (sig-figs) • 909  3 sig-figs • 7.05  3 sig-figs • 0s that are BOTH at end of number and after decimal point • 34.0  3 sig-figs • 60.00  4 sig-figs

Significant Figures(cont.) Numbers that are NOT significant: • Leftmost 0s in front of non-0 digits • 0.005  1 sig-fig • use scientific notation for these i.e. 5 x 10-3 __________________________________________ • Unlimited sig-figs occur when: • Counting; i.e. exactly 30 students • Definite quantities within system of measurements • Ex: 60 minutes in 1 hour

Significant Figures(cont.) • Calculated answers CANNOT be more accurate than the least accurate measurement from which it is calculated. • In other words: The calculated answer can’t be more accurate than the numbers you started with. RULE FOR MULTIPLICATION & DIVISION: • Number of sig-figs in answer = least number of sig-figs in input values • Example: 7.75m x 5.4m = 41.85m2 CORRECT ANSWER= 42m2  measurement with least sig-figs (5.4) only had 2 sig-figs so answer must as well RULE FOR ADDITION & SUBTRACTION: • Number of sig-figs in answer = least number of decimal places in input values • Example: 12.52m+349.0m+8.24m=369.76m CORRECT ANSWER= 369.8m measurement with least number of digits to right of decimal point dictates number of digits to right of decimal point in answer

Example 1.4 • A tortoise races a rabbit by walking with a constant speed of 2.51 cm/s for 52.23 s. How much distance does the tortoise cover? KNOWNS: UNKNOWNS: v = 2.51 cm/s d = ? t = 52.23 s d =vt = (2.51 cm)(52.23s) = 131.0973 cm =131 cm s NOW DO PRACTICE PROBLEM 24. What is the area of a circle with a radius of 12.77 m? Recall that A = π(r2)

Practice Problem 24 • What is the area of a circle with a radius of 12.77 m? Recall that A = π(r2) • A = π(12.77 m)2 = 512.3 m2 • NOW DO THE FOLLOWING PROBLEM (answer in cm) • 12.862 cm + 0.0052 m + 9.10 cm

Scientific Notation Specifies the Number of Significant Figures • SCIENTIFIC NOTATION- a method used to express numerical values as a number between 1 and 10 times an appropriate power of ten • Used to save time and effort when dealing with very small or very large numbers • m x 10nwhere 1 £ m < 10 and n=integer Writing a number in sci. not.- ex: 123,000,000,000 • To find m, put the decimal after the first digit and drop the zeroes • To find n, count the number of places from the decimal to the end of the number answer: 1.23 x 1011 • Also may be written as: 1.23E+11 or as 1.23 X 10^11

Dimensions of Some Common Physical Quantities