Dimensions of Some Common Physical Quantities QuantityDimensions Distancex(length) Area (a)x2x2 Volumex3x3 Velocity (v)x/t (length/time) Acceleration (a)x/t 2 How to interpret this: Ex: a = x t 2 So, which of the following quantities have dimensions of acceleration? a) a = xt 2 b) a = v 2 /x c) a = x/t 2 d) 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 –  3 sig-figs –  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 –  4 sig-figs

Significant Figures (cont.) Numbers that are NOT significant: Leftmost 0s in front of non-0 digits –  1 sig-fig use scientific notation for these i.e. 5 x __________________________________________ 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 = 41.85m 2 CORRECT ANSWER= 42m 2  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 s. How much distance does the tortoise cover? KNOWNS:UNKNOWNS: v = 2.51 cm/sd = ? t = s d =vt = (2.51 cm)(52.23s) = cm = 131 cm s NOW DO PRACTICE PROBLEM 24. What is the area of a circle with a radius of m? Recall that A = π(r 2 )

Practice Problem 24 What is the area of a circle with a radius of m? Recall that A = π(r 2 ) A = π(12.77 m) 2 = m 2 NOW DO THE FOLLOWING PROBLEM (answer in cm) cm m 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 10 n where 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 – Also may be written as: 1.23E+11 or as 1.23 X 10^11