Chapter 1 Units, Vectors Units, Vectors

Theories and Experiments The goal of physics is to develop theories based on experiments The goal of physics is to develop theories based on experiments A theory is a “guess,” expressed mathematically, about how a system works A theory is a “guess,” expressed mathematically, about how a system works The theory makes predictions about how a system should work The theory makes predictions about how a system should work Experiments check the theories’ predictions Experiments check the theories’ predictions Every theory is a work in progress Every theory is a work in progress

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

Systems of Measurement Standardized systems Standardized systems agreed upon by some authority, usually a governmental bodyagreed upon by some authority, usually a governmental body SI -- Systéme International SI -- Systéme International agreed to in 1960 by an international committeeagreed to in 1960 by an international committee main system used in this textmain system used in this text also called mks for the first letters in the units of the fundamental quantitiesalso called mks for the first letters in the units of the fundamental quantities

Time Units Units seconds, sseconds, s Defined in terms of the oscillation of radiation from a cesium atom Defined in terms of the oscillation of radiation from a cesium atom

US “Official” Atomic Clock

Length Units Units SI – meter, mSI – meter, m US Customary – foot, ftUS Customary – foot, ft Defined in terms of a meter – the distance traveled by light in a vacuum during a given time Defined in terms of a meter – the distance traveled by light in a vacuum during a given time

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

Standard Kilogram

Multipliers Prefixes correspond to powers of 10 Prefixes correspond to powers of 10 Each prefix has a specific name Each prefix has a specific name Each prefix has a specific abbreviation Each prefix has a specific abbreviation Larger: kilo(k), Mega (M), etc Larger: kilo(k), Mega (M), etc Small: milli (m), micro(), nano(n) Small: milli (m), micro(), nano(n)

Trigonometry Review Consider right triangle

More Trigonometry Pythagorean Theorem Pythagorean Theorem To find an angle, you need the inverse trig function To find an angle, you need the inverse trig function for example,for example, Be sure your calculator is set appropriately for degrees or radians Be sure your calculator is set appropriately for degrees or radians

Vectors in Physics Quantities with both magnitude and direction Quantities with both magnitude and direction Displacement, velocity, acceleration, force, etc.Displacement, velocity, acceleration, force, etc. Scalars with only magnitude Scalars with only magnitude Mass, energy, time, temperature, etc.Mass, energy, time, temperature, etc.

Displacement Vector Specify both magnitude and direction of physical displacement Specify both magnitude and direction of physical displacement Length dLength d Angle  (30° N of E)Angle  (30° N of E) Vector in general Vector in general Magnitude AMagnitude A Direction Direction  Coordinates Coordinates

Vector addition Graphical method Graphical method GeometryGeometry TrigonometryTrigonometry Ex. Joe heads 4 blocks north & then heads 4 blocks east Ex. Joe heads 4 blocks north & then heads 4 blocks east a)Graphical method b)Geometrical method

Vector Addition Component Method Component Method Rectangular componentsRectangular components Add the corresponding componentsAdd the corresponding components Back to magnitude angle formBack to magnitude angle form Vector subtraction Vector subtraction

Example Joe heads 100 m north & then heads 50 m 30° N of E. a) Magnitude of the displacement b) Direction

Example Let vector A be 30 m, 30° N of E. Let vector B be 30 m, 30° S of E. Find A-B.

Scientific notation Expresses large & small numbers in power of 10 Expresses large & small numbers in power of 10 Addition & subtraction Addition & subtraction Only with the same exponentOnly with the same exponent Change to the same exponentChange to the same exponent Multiplication & division Multiplication & division