Chapter 1 Introduction Ying Yi PhD PHYS I @ HCC

What does Physics do? Develop Theory by experiment Predict experiment results More experiments Check prediction PHYS I @ HCC

Outline Fundamental quantities & dimension analysis Uncertainty in measurements (significant figures) Coordinate system Problem solving strategy PHYS I @ HCC

Fundamental Quantities and Their Dimension Length [L] Mass [M] Time [T] Other physical quantities can be constructed from these three PHYS I @ HCC

Units To communicate the result of a measurement for a quantity, a unit must be defined Defining units allows everyone to relate to the same fundamental amount PHYS I @ HCC

Systems of Measurement Standardized systems Agreed upon by some authority, usually a governmental body SI – Systéme International Agreed to in 1960 by an international committee Main system used in this text PHYS I @ HCC

Length Units SI – meter, m Defined in terms of a meter – the distance traveled by light in a vacuum during a given time Also establishes the value for the speed of light in a vacuum PHYS I @ HCC

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Mass Units SI – kilogram, kg Defined in terms of kilogram, based on a specific cylinder kept at the International Bureau of Weights and Measures PHYS I @ HCC

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Standard Kilogram PHYS I @ HCC

Time Units seconds, s Defined in terms of the oscillation of radiation from a cesium atom PHYS I @ HCC

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Other Systems of Measurements cgs – Gaussian system Named for the first letters of the units it uses for fundamental quantities US Customary Everyday units Often uses weight, in pounds, instead of mass as a fundamental quantity PHYS I @ HCC

Prefixes Prefixes correspond to powers of 10 Each prefix has a specific name Each prefix has a specific abbreviation PHYS I @ HCC

Structure of Matter Matter is made up of molecules The smallest division that is identifiable as a substance Molecules are made up of atoms Correspond to elements PHYS I @ HCC

More structure of matter Atoms are made up of Nucleus, very dense, contains Protons, positively charged, “heavy” Neutrons, no charge, about same mass as protons Protons and neutrons are made up of quarks Orbited by Electrons, negatively charges, “light” Fundamental particle, no structure PHYS I @ HCC

Structure of Matter PHYS I @ HCC

Dimensional Analysis Technique to check the correctness of an equation Dimensions (length, mass, time, combinations) can be treated as algebraic quantities Add, subtract, multiply, divide Both sides of equation must have the same dimensions PHYS I @ HCC

Example 1.1 Analysis of an equation Show that the expression v=v0+at is dimensionally correct, where v and v0 represent velocities, a is acceleration, and t is a time interval. PHYS I @ HCC

Example 1.2 Find an equation Find a relationship between a constant acceleration a, speed v, and distance r from the origin for a particle traveling in a circle. PHYS I @ HCC

Outline Fundamental quantities & dimension analysis Uncertainty in measurements (significant figures) Coordinate system Problem solving strategy PHYS I @ HCC

Uncertainty in Measurements There is uncertainty in every measurement, this uncertainty carries over through the calculations Need a technique to account for this uncertainty We will use rules for significant figures to approximate the uncertainty in results of calculations PHYS I @ HCC

Significant Figures A significant figure is a reliably known digit All non-zero digits are significant Zeros are significant when Between other non-zero digits After the decimal point and another significant figure Can be clarified by using scientific notation PHYS I @ HCC

Operations with Significant Figures When multiplying and dividing, the number of significant figures in the final result is the same as the number of significant figures in the least accurate of the factors being combined When adding or subtracting, round the result to the smallest number of decimal places of any term in the sum PHYS I @ HCC

Operations with Significant Figures, rounding If the last digit to be dropped is less than 5, drop the digit If the last digit dropped is greater than or equal to 5, raise the last retained digit by 1 PHYS I @ HCC

Example 1.3 Carpet Calculations Several carpet installers make measurements for carpet installation in the different rooms of a restaurant reporting their measurements with inconsistent accuracy, as compiled in Table 1.6. compute the areas for (a) the banquet hall, (b) the meeting room, and (c) the dining room, taking into account significant figures. (d) what total area of carpet is required for these rooms? PHYS I @ HCC

Conversion of units When units are not consistent, you may need to convert to appropriate ones See the inside of the front cover for an extensive list of conversion factors Units can be treated like algebraic quantities that can “cancel” each other Example: PHYS I @ HCC

Examples 1.4 & 1.5 28.0 m/s= mi/h? 22.0 m/s2= km/min2 PHYS I @ HCC

Estimates Can yield useful approximate answers An exact answer may be difficult or impossible Mathematical reasons Limited information available Can serve as a partial check for exact calculations PHYS I @ HCC

Order of Magnitude Approximation based on a number of assumptions May need to modify assumptions if more precise results are needed Order of magnitude is the power of 10 that applies PHYS I @ HCC

Outline Fundamental quantities & dimension analysis Uncertainty in measurements (significant figures) Coordinate system Problem solving strategy PHYS I @ HCC

Coordinate Systems Used to describe the position of a point in space Coordinate system consists of A fixed reference point called the origin, O Specified axes with scales and labels Instructions on how to label a point relative to the origin and the axes PHYS I @ HCC

Types of Coordinate Systems Cartesian Plane polar PHYS I @ HCC

Cartesian coordinate system Also called rectangular coordinate system x- and y- axes Points are labeled (x,y) PHYS I @ HCC

Plane polar coordinate system Origin and reference line are noted Point is distance r from the origin in the direction of angle  from reference line Points are labeled (r,) PHYS I @ HCC

Trigonometry Review PHYS I @ HCC

More Trigonometry Pythagorean Theorem r2 = x2 + y2 To find an angle, you need the inverse trig function For example, q = sin-1 0.707 = 45.0° PHYS I @ HCC

Degrees vs. Radians Be sure your calculator is set for the appropriate angular units for the problem For example: tan -1 0.5774 = 30.00° tan -1 0.5774 = 0.5236 rad PHYS I @ HCC

Rectangular  Polar Rectangular to polar Polar to rectangular Given x and y, use Pythagorean theorem to find r Use x and y and the inverse tangent to find angle Polar to rectangular x = r cos  y = r sin  PHYS I @ HCC

Example 1.9 Cartesian and Polar Coordinates (a) The Cartesian coordinates of a point in the xy-plane are (x, y)=(-3.50 m, -2.50 m), as shown in Active Figure 1.7. Find the polar coordinates of this point. (b) Convert (r, )=(5.00 m, 37.0o) to rectangular coordinates. PHYS I @ HCC

Outline Fundamental quantities & dimension analysis Uncertainty in measurements (significant figures) Coordinate system Problem solving strategy PHYS I @ HCC

Problem Solving Strategy PHYS I @ HCC