Chapter 1: INTRODUCTION

Physics: branch of physical science that deals with energy, matter, space and time. Developed from effort to explain the behavior of the physical environment. Summary: laws of Physics, Formula, graphs. Basis of rocket/space travel, modern electronics, lasers, medical science etc. Major goal: reasoning critically (as a physicist), sound conclusions, applying the principles learnt. We will use carefully defined words, e.g. velocity, speed, acceleration, work, etc.

Factor (or ratio) – number by which a quantity is multiplied or divided when changed from one value to another. Eg. The volume of a cylinder of radius r and height h is V =  r 2 h. If r is tripled, by what factor will V change? V old =  r 2 h, V new =  (3r) 2 h = 9.  r 2 h, V new /V old = 9. V will increase by a factor of 9. (a)Decreasing the number 120 by 30% gives ---- (b)Increasing the number 120 by 30% gives § 1.3: The Use of Mathematics

Proportion If two quantities change by the same factor, they are directly proportional to each other. A  B – means if A is doubled, B will also double. S  r 2 – means if S is decreased by factor 1/3, r 2 (not r!) will also decrease by the same factor.

Inverse Proportion If A is inversely proportional to B – means if A is increased by a certain factor, B will also decrease by the same factor. K inversely proportional to r [K  1/r] – means if r is increased by factor 3, K will decrease by the same factor. The area of a circle is A =  r 2. (a)If r is doubled, by what factor will A change? (b)If A is doubled, by what factor will r change?

§ 1.4: Scientific notation: Rewriting a number as a product of a number between 1 and 10 and a whole number power of ten. Helps eliminate using too many zeros. Helps to correctly locate the decimal place when reporting a quantity. Eg: Radius of earth = 6,380,000 m = 6.38 x 10 6 m Radius of a hydrogen atom = m = 5.3 x m.

In reporting a scientific measurement, it is important to indicate the degree of precision and the accuracy of your measurement. This can be done using absolute (or percentage) error, significant figures and order of magnitude, etc. Precision/Accuracy in Scientific Measurements

(a)Absolute/Percentage error: Eg. Length of a notebook = 27.9 ± 0.2 cm  Actual length is somewhere between 27.9 – 0.2 and , ie 27.7 and 28.1 cm  ± 0.2 is the estimated uncertainty (error).  0.2 is the absolute uncertainty (error).  27.9 is the central value  27.7 and 28.1 are called extreme values.

Percentage Uncertainty  Percentage uncertainty = Eg. Length of a notebook = 27.9 ± 0.2 cm % Uncertainty = Fractional Error

The length of a table was found to be 1.5 m with 8% error. What was the absolute error (uncertainty) of this measurement? The mass of a bag was found to be 12.5  0.6 kg. What was the percent error in this measurement? Examples

Error Propagation in Addition/Subtraction The absolute error in the sum or difference of two or more numbers is the SUM of the absolute errors of the numbers. Eg. 8.5  0.2 cm and 6.9  0.3 cm Sum = 15.4  0.5 cm Difference = 1.6  0.5 cm

Error Propagation in Multiplication/Division The fractional error in the product or quotient of two numbers is the SUM of the fractional errors of the numbers.

Error Propagation in Multiplication/Division Eg. x = 8.5  0.2 cm and y = 6.9  0.3 cm Fractional errors: in x = = in y = = Find the product, P = x.y and its absolute uncertainty (  P).

Examples The area of a circle is A =  r 2. (a)If r is doubled, by what factor will A change? (b)If A is doubled, by what factor will r change?

(b) Significant Figures: Number of reliably known digits in a measurement. Includes one “doubtful” or estimated digit written as last digit. Eg [6 is the last digit. It is the doubtful digit]. Eg [8 is the last digit. It is the doubtful digit].

All nonzero digits are significant. Zeros in between significant figures are significant.[2,508] Ending zeros written to the right of the decimal point are significant. [ ] Zeros written immediately on either sides of decimal point for identifying place value are not significant. [0.0258, 0.258] Zeros written as final digits are ambiguous.[25800] To remove ambiguity, rewrite using scientific notation. Eg. (i) – 4 sf, (ii) – 3 sf, (iii) x 10 5 – 4 sf. (iv) – 2.58x 10 4 = 3 sf, 2.580x 10 4 = 4 sf, x 10 4 = 5 sf. Significant Figures contd:

Significant Figures in Addition/Subtraction The sum/difference can not be more precise than the least precise quantities involved. ie, the sum/difference can have only as many decimal places as the quantity with the least number of decimal places. Eg: 1) m m m = 2) 77.8 kg – kg = “keep the least number of decimal places”

Significant Figures in Multiplication/Division The product/quotient can have only as many sf as the number with the least amount of sf. Eg: 1) What is the product of m and m? 2) What is 568 m divided by 2.5 s? “keep the least number of significant figures”

– (roughly what power of ten?) To determine the order of magnitude of a number: Write the number purely as a power of ten. Numbers < 5 are rounded to 10 0 Numbers  5 are rounded to10 1 Eg. 754 =7.54 x 10 2 ~10 1 x 10 2 = The order of magnitude of 754 is ,179 = x 10 5 ~10 0 x 10 5 = 10 5 = 5 O/M ~ orders of magnitude = - 2 (how?). (c) Order of Magnitude

What is the difference between accuracy and precision?

Precision: Reproducibility or uniformity of a result. Indication of quality of method by which a set of results is obtained. A more precise instrument is the one which gives very nearly the same result each time it is used. A precise data may be inaccurate!! Accuracy: How close the result is to the accepted value. Indication of quality of the result. A more accurate instrument is the one which gives a measurement closer to the accepted value.

Precise/Accurate Precise/Not Accurate Not Precise/Not Accurate Not Precise/Accurate

§ 1.5: Units We will use the SI system of units which is an international system of units adapted in 1960 by the General Council of Weights and Measures. In SI system: Length is measured in meters (m). Mass is measured in kilograms (kg). Time is measured in seconds (s).

Other fundamental quantities and their units in the SI system includes Temperature (in Kelvin, K), Electric current (in Amperes, A) Amount of substance (in mole, mol) and Luminosity (in Candela, cd). The SI system is part of the metric system which is based on the power of ten.

Converting Between Units Eg. Convert 65 miles/hour to SI units. 1 mile = km = 1609 m. 1 hour = 3,600 seconds

§ 1.6: Dimensional Analysis Dimensions – Units of basic (Fundamental) quantities: Mass [M], Length [L], Time [T] We can only add, subtract or equate quantities with the same dimensions.

Eg. 1 Check if the expression v = d 2 /t is correct, where v = speed (in m/s), d is the distance (in m) and t is time (in s). Quantity Dimension V d 2 [L] 2 T [T] v = d 2 /t Hence eqn is not correct

Eg. 2: If the equation was now correctly written as v = kd 2 /t, what must be the units of k? The units of k must be m -1

§ : Reading Assignment