Pre-AP Physics Chapter 1 Notes Yockers JHS 2008

Pre-AP Physics Chapter 1 Notes Yockers JHS 2008 Standards o Length, Mass, and Time ( - length quantities) - mass - time Derived Quantities: Examples Dimensional Analysis useul to check equations and to assist in deriving expressions - L = length; M = mass; and T = time Conversion o Units multiplying a quantity by a conversion actor ( ) with numerator and denominator having dierent units to provide the desired units in the inal result. Importance?! Geometry / Trigonometry / Algebra Signiicant Figures measured values are known only to within the limits o experimental uncertainty (quality o apparatus, skill o experimenter, number o measurements) - When,the number o signiicant igures in the inal answer is the same as the number o signiicant igures in the quantity having the number o signiicant igures. - When numbers are, the number o decimal places in the result should equal the smallest number o decimal places o any term in the sum. - Ater you are done with Chapter 1 (and or the AP Exam) signiicant igures is a good guideline. Coordinate Systems used to speciy locations in space consist o - a ixed reerence point O, called the - a set o speciied axes or directions with - instructions that explain how to label a point in space relative to the origin and axes - the (rectangular) and/or coordinate systems will be used unless speciied Vectors and Scalars - scalar a quantity that is completely speciied by a positive or negative number with appropriate - vector a quantity that must be speciied by both since velocity, v, is a vector, it should be written as either v or velocity s magnitude (always positive) could be written as v or

Pre-AP Physics Chapter 2 Notes Yockers JHS 2008 KINEMATICS (1-Dimensional Motion) Motion/Strobe diagrams Importance o coordinate systems and speciying direction o vectors Displacement - displacement or an object at rest = - displacement can be positive or negative - displacement does not equal (general) where d = displacement (change in position) (horizontal) (vertical) - displacement has both magnitude and direction (vector) vector is a physical quantity that requires the speciication o both scalar is a quantity that has Velocity the quantity that measures how Average velocity total displacement divided by the time interval during which the displacement occurred (m/s) - speed does not equal velocity has magnitude and direction, and speed only has - average velocity can equal slope i s and t are graphed steeper slope = position-time graph that is parallel to time axis (x axis) has a position that does not change over time (velocity o m/s) - slope allows you to determine v avg over short or long time intervals instantaneous velocity the limit o the average velocity as the time interval t becomes ininitesimally short the slope o the line tangent to the position-time curve at a given point is the instantaneous velocity at that corresponding time instantaneous speed (scalar) is deined as the magnitude o the instantaneous velocity (speed can never be negative) - equation o motion or average velocity

Pre-AP Physics Chapter 3 Notes Yockers JHS 2008 KINEMATICS (1-Dimensional Motion) Acceleration - velocity-time graphs - motion/strobe diagrams Average acceleration the change in velocity divided by the time interval during which the change occurs (m/s)/s = m/s 2 - acceleration is a vector quantity (direction and magnitude) - acceleration can be either when an object s velocity and acceleration are in the object with time when an object s velocity and acceleration are in object with time direction, the speed o the directions, the speed o the One-dimensional motion with constant acceleration - when acceleration is constant, average acceleration equals instantaneous acceleration - or constant acceleration (inal velocity with average acceleration) or - since velocity is increasing or decreasing uniormly with time (constant a), the average velocity in any time interval can be expressed as the arithmetic average o the initial velocity and the inal velocity - now we can determine the displacement o an object as a unction o time d = d i + v avg t = d i vi + v + 2 t 1 = d i + 2 ( v i + v ) t or, by substituting v = v i + a avg t remember, this is or a constant a - to relate displacement, velocity, and acceleration without time (d i is usually considered to be 0)

Free-all - a reely alling object is an object moving under the inluence o only, regardless o its initial motion - objects thrown upward or downward and those released rom rest are all alling reely once they are - once in ree-all, all objects have an acceleration, which is the ree-all acceleration g ( m/s 2 ) - all o the previous ormulas can be applied to ree-all situations by replacing the general displacement symbol s with the vertical displacement symbol y

Pre-AP Physics Chapter 4 Notes Yockers JHS 2008 Forces In One Dimension (Newton s Laws) Force represents the interaction o an object with its - orces cause - SI unit or orce is the newton (N) 1 N equals the amount o orce that, when acting on a 1 kg mass, produces an acceleration o 1 m/s 2 1 N = 1 kg x 1 m/s 2 F = ma - orces can act through contact orces ield orces exists between objects - gravity (gravitational ield) - electricity (electric ield) - magnetism (magnetic ield) undamental orces that act on elementary particles are all ield orces - orce depends upon (orce is a quantity) - diagrams that show orce vectors as arrows are called - ree-body diagrams are used to analyze only the orces aecting the motion o Newton s First Law - what is the motion o an object beore orces are applied? will an object with no orce acting on it always be at rest? - Galileo realized (1630s) that a block sliding on a perectly smooth surace would in the absence o an an object s nature is to maintain its Newton developed this idea urther - Newton s irst law (the Law o Inertia) when the net external orce on an object is, its acceleration is inertia the tendency o an object net external orce can be determined by a - an object s change in motion is the same as i the were the only orce acting on the object external orce is a single orce that acts on an object as a result o the interaction between the object and its environment net external orce is the - mass is a measurement o in a body which has more inertia? - bowling ball or a gol ball? - ootball: lineman or runningback? inertia is directly proportional to - mass body accelerates under an applied orce - equilibrium the state o a body in which there is - Newton s irst law describes equilibrium a body is in equilibrium when

Newton s Second Law orce is proportional to - the acceleration o an object is directly proportional to the net external orce acting on the object and inversely proportional to the mass o the object F a (constant m) m a (constant F) or i the net external orce is zero, then - - - Newton s Third Law orce always exists in pairs (action-reaction pair); - i two bodies interact, the magnitude o the orce exerted on object 1 by object 2 is equal to the magnitude o the orce simultaneously exerted on object 2 by object 1, and the two orces are opposite in direction - or every action there is an action-reaction pair remember, reaction orce occurs at as the action orce thus, either orce can be considered either the action orce or the reaction orce - action-reaction pairs may not result in equilibrium because they act Weight measure o the magnitude o exerted on an object - 1 lb = 4.448 N - 1 N = 0.225 lb - F g (W) is the orce exerted by the Earth on an object ( ) because weight is dependent on gravity, weight depends on remember, does not change weight is not an inherent property o an object objects weigh less at higher altitudes because a g decreases with increasing distance rom the center o the Earth Normal Force (F N ) - normal also means - normal orce is a contact orce exerted by one object on another in a direction perpendicular to the

Pre-AP Physics Chapter 5 Notes Yockers JHS 2008 Forces in Two Dimensions Force o Friction - F s is the orce o - F s,max occurs when the applied is as great as it can be without causing an object to (the orce o static riction reaches its maximum value) - F k is the orce o kinetic riction which will be less than F s,max because (cold-welding; intermolecular orces between an object and a surace) cannot orm - orce o riction also depends on the o the suraces in contact - coeicient o riction (µ) o the orce o riction to the normal orce acting between two objects -coeicient o riction is a ratio o orces ( ) µ k will always be lower than µ s a value o 1.0 or µ s indicates Air Resistance (F R ) acts in the direction to an object s motion - magnitude o F R, F R, is usually proportional to the F R v - when F R = F in the opposite direction, a = 0 m/s 2 - in reeall, when F R = F g, a = 0 m/s 2, ( ) has been reached

Pre-AP Physics Chapter 6 Notes Yockers JHS 2008 MOTION IN TWO DIMENSIONS Free-all - a reely alling object is an object moving under the inluence o only, regardless o its - objects thrown upward or downward and those released rom rest are all alling reely once they are - once in ree-all, all objects have, which is the ree-all acceleration g ( ) - all o the kinematic ormulas can be applied to ree-all situations by replacing the general displacement symbol d with the vertical displacement symbol y Projectile Motion (2-Dimensional) - assumptions the ree-all acceleration, a g or g, has a magnitude o 9.8 m/s 2, is over the range o motion, and is directed (so a g or g = -9.8 m/s 2 ) the eect o air resistance is the rotation o the Earth - motion in the x direction (constant no ) - motion in the y direction - speed o the projectile and its direction at any instant can be calculated rom the components o the velocity at that instant

Circular Motion - or an object moving in a circular path with a, acceleration is due to a change in - centripetal acceleration v v0 remember a = and that velocity can be changed either by or t t 0 ; a change in either produces centripetal acceleration (a c ) acceleration directed toward the - magnitude o a c is given by Causes o Circular Motion - orces maintain circular motion an object in a circular path is accelerating because the direction (not magnitude) o its velocity is the acceleration is the o an object would preer a straight-line path but centripetal acceleration maintains a the magnitude o the orce causing the centripetal acceleration can be calculated by - a orce directed toward the is necessary or circular motion orce acting to motion will change velocity i this orce vanishes, motion begins tangent to the circular path - ree-all? - projectile motion? - inertia is oten misinterpreted as a mobile phone on dash board - is riction enough to hold it in place? - side o care will provide enough orce to put the mobile phone into the circular path the car is ollowing Relative Velocity Problems there is no set way o attacking these problems, so be sure you practice!

Pre-AP Physics Chapter 7 & 8 Notes Yockers JHS 2008 The Law o Gravity and Rotational Motion Newton s Universal Law o Gravitation - planets move in nearly circular orbits around the Sun - gravitational orce causes these nearly circular orbits - gravitational orce is the natural orce o attraction between any two objects in the universe (a ield orce) not just large objects (stars, planets, etc.) gravitational orce acts in the o the undamental orces the gravitational orce is always Newton s law o universal gravitation every particle in the Universe attracts every other particle with a orce that is directly proportional to the product o the masses o the particles and inversely proportional to the square o the distance between them - G = 6.67 x 10-11 N m 2 /kg 2 (the universal gravitational constant) - r is the distance between the o the two particles the gravitational ield at the surace o a planet - i r is equal to the radius o the planet, this equation gives the acceleration due to gravity at the o the planet Rotational quantities - rotational motion motion o a body that - axis o rotation - circular motion occurs when any single point on an object travels in a circle around an axis o rotation r radius s arc length - angles can be measured in radians radian an angle whose arc length is equal to its radius 360 rad = radian(s); 1 rad = arc length / length o radius when s=r; 1 rad = 57. 3 2π the radian is in general, any angle, θ, measured in radians, is deined by the relation conversions

- angular displacement, θ, describes how much an object has the angle through which a point, line, or body is rotated in a speciied direction and about a speciied axis θ - angular displacement - s is positive (+) when rotation is - s is negative (-) when rotation is - angular speed, ω, describes the rate at which a body rotates about an axis, usually expressed in average angular speed = ω avg unit is rad/s or revolutions/unit time - angular acceleration, α, occurs when the time rate o change o angular speed, expressed in rad/s/s or rad/s 2 average angular acceleration = α avg - all points on a rotating rigid object have the same angular acceleration and angular speed i not, - similarities o angular and linear quantities linea angular r x θ v ω a α Comparing angular and linear quantities - linear kinematics v d v 2 = v 0 1 = d 0 + v0t + at 2 = v + 2a( d) 2 0 + a t - angular kinematics 2 Tangential and centripetal acceleration - objects in circular motion have a - an object arther rom the axis o rotation must travel at a tangential speed around the circular path, s, to travel the same as would an object closer to

the axis - tangential speed ω must be measured in rad / s - tangential acceleration is tangent to the the instantaneous linear acceleration o an object directed along the tangent to the object s circular path α must be measured in rad 2 / s - centripetal acceleration v v0 remember a = and that velocity can be changed either by t t 0 ; a change in either produces or an object moving in a circular path with a constant speed, acceleration is due to a change in centripetal acceleration (a c ) acceleration directed toward the o a circular path - magnitude o a c is given by or - because tangential speed is related to the angular speed by v t = rω, the centripetal acceleration can also be ound using angular speed - tangential and centripetal accelerations are tangential component o acceleration is due to changing centripetal component o acceleration is due to changing - total acceleration is ound using the Pythagorean theorem - direction o the acceleration can be ound using Causes o Circular Motion - orces maintain circular motion an object in a circular path is accelerating because the direction (not magnitude) o its velocity is constantly changing the acceleration is centripetal or directed toward the center o motion

the inertia o an object would preer a path but centripetal acceleration maintains a path the magnitude o the orce causing the centripetal acceleration can be calculated by - a orce directed toward the is necessary or circular motion orce acting to motion will change i this orce vanishes, straight-line motion begins tangent to the circular path - ree-all? - projectile motion? - inertia is oten misinterpreted as a orce mobile phone on dash board - is riction enough to hold it in place? - side o care will provide enough orce to put the mobile phone into the circular path the car is ollowing Torque - τ (tau) SI derived unit is N m - point mass vs. extended object extended object has a point mass assuming all o an object s mass is - rotational and translational motion can be separated translational motion rotational motion - net torque produces rotation torque a quantity that measures the ability o a orce to an object about some axis - torque depends on how easily an object rotates depends not only on how much orce is applied but also on the orce is applied lever arm the distance rom the axis o rotation to a line drawn along the direction o the orce - torque also depends on the orces do not have to be to cause rotation

- two equal but opposite orces can produce a rotational acceleration i they do not act along the same line - i torques are equal and opposite, there will be no rotational acceleration seesaw momentary torque produced by pushing with legs Rotational Equilibrium - equilibrium requires i the net orce on an object is zero, the object is in equilibrium i the net torque on an object is zero, the object is in equilibrium - the dependence o equilibrium on the absence o net torque is called the second condition o equilibrium the resultant torque acting on an object in rotational equilibrium is independent o where the axis is placed - an unknown orce that acts along a line passing through this axis o rotation will - beginning a diagram by arbitrarily setting an axis where a orce acts can eliminate an unknown in a problem - conditions or equilibrium Type o Equation Symbolic Eq. Meaning translational ΣF net =0 F net on an object must be zero rotational Στ net =0 τ net on an object must be zero - unstable equilibrium - stable equilibrium

Pre-AP Physics Chapter 9 Notes Yockers JHS 2008 Momentum & Impulse Momentum describes an object s - a vector quantity deined as the product o an object s p is momentum direction matches that o derived unit = - a change in momentum takes momentum is closely related to Impulse or a constant external orce, the product o the orce and the time over which it acts on an object - impulse-momentum theorem F t = = impulse is a - all orces exerted on an object are assumed unless otherwise noted - stopping times and stopping distances depend on the impulse momentum theorem - a change in momentum over a longer time requires less orce Conservation o Momentum - momentum is always - law o conservation o momentum the total momentum o all objects interacting with one another remains constant regardless o the nature o the orces between the objects momentum is conserved in momentum is conserved or objects - Newton s third law leads to conservation o momentum or the orces in a collision involving two objects momentum and the collision - orces involved in a collision are treated as though they are in a real collision things are a bit more complicated! we work with average orces

Elastic and Inelastic collisions - two extreme types o collisions - perectly inelastic collision a collision in which two objects and move with a ater colliding objects become essentially inal mass is equal to the move with the remember, signs or direction are important! K does not remain constant in inelastic collisions - some K is converted to heat, sound, internal K, and internal U (deormation, etc.) - elastic collision a collision in which the objects maintain their original shapes and are not by the action o orces - most collisions are neither elastic nor perectly inelastic - most collisions all into a category between the two extremes inelastic collisions colliding objects bounce and move separately ater the collision, but K decreases in the collision - K and p are both conserved in remember, signs (+/-) are important - glancing collisions colliding masses rebound at some relative to the line o motion o the incident mass momentum is conserved in all collisions when no external orces are acting total momentum is conserved along the and

Pre-AP Physics Chapter 10 Notes Yockers JHS 2008 Work & Energy Work a orce that causes a displacement o an object does - using d instead o s work equals the magnitude o the orce, F, times the magnitude o the work is not done unless an object is due to the action o a orce the o a orce alone does not constitute work - work is done only when components o a orce are to a displacement the component to the direction o an object s displacement does work components to a displacement do no work - derived unit or work is the joule (J) or N m (ater James Prescott Joule 1818-1889) - the sign o work is important work is scalar and can be + or - - work is positive when the component o orce is in the as the displacement - work is negative when the orce is in the direction the displacement - cosθ is negative or angles greater than 90 but less than 270 - cosθ is positive or angles less than 90 but greater than 270 perpendicular to direction o displacement - cos(90 ) = - cos(270 ) = - i the work done on an object results only in a change in the object s speed, the sign o the net work indicates whether speed is increasing or decreasing + work in speed and orce ect - work in speed and Energy - kinetic energy (K) associated with an object in K is a scalar quantity dependent upon SI unit is the joule (J) or N m Work, Energy, and Power - work-kinetic energy theorem relates the work done on an object to the change in kinetic energy work is a method o transerring - power

and since W = Fd SI unit or power is the watt (W) (James Watt 1736-1819) - 1 W = 1 J/s - 1 horsepower = 746 W machines with dierent power ratings do the same work in Simple Machines - machine any device that transmits or modiies orce, usually by changing the orce applied to an object - all machines are combinations o six undamental types o machines (simple machines) - mechanical advantage comparison o how large the is relative to - claw hammer example - machines can alter the orce and the distance moved, but the work done on the object (product o F x d) is - mechanical advantage o an ideal machine in a real system, some o the work done by the orce is - eiciency is a measure o how well a machine works eiciency is a measure o how much input energy is lost (riction) compared with how much energy is used to perorm eiciency o an ideal machine is eiciency also equal to the mechanical advantage divided by the ideal mechanical advantage

Pre-AP Physics Chapter 11 Notes Yockers JHS 2008 Energy and Its Conservation Energy - kinetic energy (K) associated with K is a scalar quantity dependent upon SI unit is the joule (J) or N m - potential energy (U) stored energy energy associated with an object due to describes an object that has the potential to move because o depends not only on the properties o an object but also on the object s U is a scalar quantity SI unit is the joule (J) or N m - gravitational potential energy (U g ) depends on potential energy associated with an object due to its position relative to the Earth o some other gravitational source note that a g and h are o an object U g is a result o an object s position, so it must be measured relative to some where U g = - elastic potential energy (U s ) depends on distance the potential energy in a stretched or compressed elastic object - elastic capable o recovering relaxed length the length o a spring when no external orces are acting on it - k is the spring constant or orce constant a parameter that expresses how a spring (or elastic material) is to being SI unit is N/m - x is the distance compressed or stretched - mechanical energy (ME) the sum o and all orms o associated with an object or group o objects is not a unique orm o energy like the energies listed above is not necessarily related to all energy that is not mechanical energy is classiied as energy -

Conservation o Energy - conserved quantity remains constant but may change - conservation o mechanical energy in the absence o riction, mechanical energy remains the same mathematical expression depends on the orms o energy in a given situation conservation o energy occurs even when acceleration varies as long as - mechanical energy is not conserved in the presence o total energy is always conserved heat energy is not mechanical, so energy is lost rom the mechanical energy system KE in Elastic and Inelastic Collisions - momentum is always - law o conservation o momentum the total momentum o all objects interacting with one another remains constant regardless o the nature o the orces between the objects momentum is conserved in momentum is conserved or objects - perectly inelastic collision a collision in which two objects stick together and move with a common velocity ater colliding K does not remain constant in - some K is converted to heat, sound, internal K, and internal U (deormation, etc.) - elastic collision a collision in which the total momentum and the total K remain constant K and p are both conserved in

Pre-AP Physics Chapter 12 Notes Yockers JHS 2008 Thermal Energy Deining Temperature - adding or removing energy changes - temperature is proportional to the o atoms/molecules monatomic gases other substances molecules can rotate and/or vibrate - - - - temperature is meaningul only when it is (zeroth law o thermodynamics) thermal equilibrium the state in which two bodies in physical contact with each other have - basis or measuring temperature with thermometers - the temperature o any two objects at thermal equilibrium always - matter expands as its temperature thermal expansion as the temperature o a substance increases, so does its - thermal expansion characteristics o a material are indicated by a quantity called the - between 0 C and 4 C the volume o water - measuring temperature calibrating thermometers requires - ice point (0 C) mixture o water and ice at 1 atm - steam point (100 C) mixture o steam and water at 1 atm - degrees are Fahrenheit (US) Celsius (centigrade) SI the possible problem with the above temperature scales is that they can have because kinetic energy, K, o atoms/molecules in a substance always has a positive value, the temperature that is a measure o that energy should also have positive magnitudes - Kelvin scale absolute zero 0 K = Heat and Energy - heat (Q) energy transerred between objects o heat (energy) moves rom a temperature to a temperature - heat has units o joules work, K, and U 1 calorie = 4.186 J (Cal = kcal) - conservation o energy

Changes in Temperature and Phase - there is a property o all substances that causes their temperatures to vary by dierent amounts when equal amounts o energy are added to or removed rom them result o the ease with which atoms and molecules within a substance - how easily the temperature o a substance can change speciic heat capacity (speciic heat) - relates - c p = - Q = - m = - T = speciic heat capacity can be used or both - - when T and Q are positive (+), energy is transerred when T and Q are negative (-), energy is transerred the substance the substance Calorimetry - uses the well know speciic heat o water (4186 J/kg C) and a calorimeter to determine speciic heat capacity o dierent substances using the ollowing relationships or w = water x = substance Latent Heat and Phase Change - all phase changes involve a change in no change in temperature ( ) there is a change in matter ( ) - the energy required to change the phase o a given mass m o a pure substance is where L is the latent heat o the substance latent heat L depends upon the L depends upon the the proper sign is chosen according to the direction o the energy low - ice to water - water to ice

- latent heats L latent heat o usion when phase change involves L v latent heat o vaporization when phase change involves latent heats vary considerably between substances and L and L v -the latent heat o vaporization or a given substance is usually larger than the latent heat o usion - in the change rom solid to liquid phase, solid bonds between molecules are transormed into somewhat weaker liquid bonds - in the change rom liquid to gas phase, however, liquid bonds are broken, creating a situation in which the molecules o the gas have essentially no bonding to one another - more energy is thereore required to vaporize a given mass o a substance than to melt it - with a knowledge o latent heat, it is possible to understand the ull behavior o a substance as energy is added to it The First Law o Thermodynamics - energy conservation requires that the total change in internal energy rom its initial to its inal equilibrium conditions be equal to the transer o energy by both heat and work remember that U = U U 0 change must be equal to the transer o energy by both - the change in internal energy o a system is zero in a cyclic process a thermodynamic process in which a system returns to the same conditions under which it started - heat engines use heat to do work The Second Law o Thermodynamics - no machine can be made that only absorbs energy by heat and then entirely transers the energy out o the engine by an equal amount o work - thermodynamic eiciency

Q h = Q c = Heat and Entropy Note will entropy (S) increase, decrease, or remain the same during a particular process - entropy a measure o the entropy can be regarded as an index o the 2 nd Law o Thermodynamics is really a statement o - the more disordered a system is, - the entropy o the Universe increases in all natural processes (another way o stating the 2 nd Law o Thermodynamics) there are processes in which the entropy o a system (A) decreases, but this must be accompanied by a net increase in entropy o some other system (B) the change in entropy o system B is greater than the change in entropy o system A