1. Motion in One Dimension

2. Reminder: Homework due Wednesday at the beginning of class Sig. figs Converting Units Order of magnitude 2.1 Reference Frame 2.2 average Velocity

3. Measurement and Uncertainty; Significant Figures Scientific notation is commonly used in physics; it allows the number of significant figures to be clearly shown. Much of physics involves approximations; these can affect the precision of a measurement also.

4. Measurement and Uncertainty; Significant Figures Conceptual Example 1-1: Significant figures. Using a protractor, you measure an angle to be 30°. (a) How many significant figures should you quote in this measurement? (b) Use a calculator to find the cosine of the angle you measured.

5. Prefixes Prefixes correspond to powers of 10 Each prefix has a specific name Each prefix has a specific abbreviation

6. Prefixes, cont. The prefixes can be used with any base units They are multipliers of the base unit Examples: 1 mm = 10 -3 m 1 mg = 10 -3 g

7. Fundamental and Derived Quantities In mechanics, three fundamental or base quantities are used Length Mass Time Will also use derived quantities These are other quantities that can be expressed as a mathematical combination of fundamental quantities

8. Density Density is an example of a derived quantity It is defined as mass per unit volume Units are kg/m 3

9. Units, Standards, and the SI System We will be working in the SI system, in which the basic units are kilograms, meters, and seconds. Quantities not in the table are derived quantities, expressed in terms of the base units. Other systems: cgs; units are centimeters, grams, and seconds. British engineering system has force instead of mass as one of its basic quantities, which are feet, pounds, and seconds.

10. Converting units 1. Multiplying by 1 leaves a quantity unchanged. 2. “1” can be represented as 3. Choose form for ‘1’ for which units match.

11. Question 1 atm = 1.013 x10 5 Pa = 14.70 lb/in 2 If you want to convert 0.46 atm to Pa you should A. Multiply 0.46 atm by 14.70 lb/in 2 B. Multiply 0.46 atm by 1.013 x10 5 Pa C. Divide 0.46 atm by 14.70 lb/in 2 D. Divide 0.46 atm by 1.013 x10 5 Pa

12. Converting units 1. You're stopped by police for speeding 30.0 km/h over the speed limit on an Ontario highway. What is the speed in mph? 2. That'll be a $180 fine, plus a $35 victim surcharge and a $5 court fee ($220 in all) should you decide to plead guilty and settle out of court. (in Canadian Dollars). What is the fine in US dollars?

13. Converting units 1. 30.0 km/h =? 1 km = 0.6214 miles 2. $220 Canadian Dollars = ? 1 US dollar = 0.97 Canadian dollar

14. Order of Magnitude: Rapid Estimating A quick way to estimate a calculated quantity is to round off all numbers to one significant figure and then calculate. Your result should at least be the right order of magnitude; this can be expressed by rounding it off to the nearest power of 10. Diagrams are also very useful in making estimations.

15. Order of Magnitude: Rapid Estimating Example 1-5: Volume of a lake. Estimate how much water there is in a particular lake, which is roughly circular, about 1 km across, and you guess it has an average depth of about 10 m.

16. Order of Magnitude: Rapid Estimating Example 1-6: Thickness of a page. Estimate the thickness of a page of your textbook. (Hint: you don’t need one of these!)

17. Coordinate Axis In Physics we draw a set of coordinate axis to represent a frame of reference. In one dimensional axis coordinate, the position of an object is given by its x coordinate. o x y -y -x

18. Position on a line 1.Reference point (origin) 2.Distance 3.Direction Symbol for position: x SI units: meters, m

19. Displacement on a line xfxf xixi Change of position is called Displacement: Displacement is a vector quantity It has magnitude and direction

20. Displacement Defined as the change in position during some time interval Represented as  x SI units are meters (m)  x can be positive or negative Different than distance – the length of a path followed by a particle. Displacement has both a magnitude and a direction so it is a vector.

21. Vectors and Scalars Vector quantities need both magnitude (size or numerical value) and direction to completely describe them Will use + and – signs to indicate vector directions Scalar quantities are completely described by magnitude only

22. Average Speed Average speed =distance traveled/ time elapsed Example: if a car travels 300 kilometer (km) in 2 hours (h), its average speed is 150km/h. Not to confuse with average velocity.

23. Average Velocity The average velocity is rate at which the displacement occurs The SI units are m/s Is also the slope of the line in the position – time graph

24. Average Velocity, cont Gives no details about the motion Gives the result of the motion It can be positive or negative It depends on the sign of the displacement It can be interpreted graphically It will be the slope of the position-time graph

25. Not to Confuse Speed is a number : a scalar Velocity is a vector : with magnitude and direction

26. Example 2-1: Runner’s average velocity. The position of a runner as a function of time is plotted as moving along the x axis of a coordinate system. During a 3.00-s time interval, the runner’s position changes from x 1 = 50.0 m to x 2 = 30.5 m, as shown. What was the runner’s average velocity? Average Velocity