Revision Guide for Chapter 11

Size: px
Start display at page:

Download "Revision Guide for Chapter 11"

Transcription

1 Revision Guide fo Chapte 11 Contents Student s Checklist Revision Notes Momentum... 4 Newton's laws of motion... 4 Gavitational field... 5 Gavitational potential... 6 Motion in a cicle... 7 Summay Diagams (OHTs) Consevation of momentum... 8 Collisions fom diffeent viewpoints... 9 Examples of collisions Momentum and foce Jets and ockets Field diection and equipotentials Centipetal acceleation Satellites and Keple s thid law Advancing Physics A 1

2 Student's Checklist Back to list of Contents I can show my undestanding of effects, ideas and elationships by descibing and explaining cases involving: momentum as the poduct of mass velocity foce as ate of change of momentum consevation of momentum when objects inteact Revision Notes: Momentum; Newton s Laws of motion Summay Diagams: Consevation of momentum; Collisions fom diffeent viewpoints; Examples of collisions; Momentum and foce; Jets and ockets wok done (as foce distance moved in the diection of the foce: including cases whee the foce does not act in the diection of the esulting motion) changes of gavitational potential enegy and kinetic enegy when objects move in a gavitational field motion in a unifom gavitational field See Revision Guide Chapte 9: Wok; kinetic enegy; potential enegy; fee fall; pojectile the gavitational field and gavitational potential due to a point mass Revision Notes: Gavitational field; Gavitational potential Summay Diagams: Field diection and equipotentials; motion in a hoizontal cicle and in a cicula gavitational obit about a cental mass Revision Notes: Motion in a cicle Summay Diagams: Centipetal acceleation; Keple s laws; Satellites and Keple s thid law I can use the following wods and phases accuately when descibing effects and obsevations: Momentum Revision Notes: Momentum kinetic enegy and potential enegy See Revision Guide Chapte 9: kinetic enegy; potential enegy gavitational field, gavitational potential Advancing Physics A

3 Revision Notes: Gavitational field; Gavitational potential I can sketch, plot and intepet: gaphs showing the vaiation of a gavitational field with distance, and know that the aea unde the gaph shows the change in gavitational potential Revision Notes: Gavitational field gaphs showing the vaiation of gavitational potential with distance, and know that the tangent to the cuve gives the gavitational field stength Revision Notes: Gavitational potential diagams illustating gavitational fields and the coesponding equipotential sufaces Summay Diagams: Field diection and equipotentials I can make calculations and estimates involving: kinetic enegy ½ mv, gavitational potential enegy change mgh enegy tansfes and exchanges using the idea: wok done E = Fs cosθ, (no wok is done when F and s ae pependicula) See Revision Guide Chapte 9: Wok; kinetic enegy; potential enegy; fee fall; pojectile momentum p = mv and F = (mv) / t Revision Notes: Momentum; Newton s Laws of motion cicula and obital motion: a = v /; F = mv / Revision Notes: Motion in a cicle Summay Diagams: Centipetal acceleation; GmM Fgav gavitational fields: F gav =, g = = m GmM gavitational potential enegy E GM gavitational potential V = gav gav = m GM Revision Notes: Gavitational field; Gavitational potential Summay Diagams: Field diection and equipotentials; Advancing Physics A 3

4 Revision Notes Back to list of Contents Momentum Momentum is mass x velocity. Momentum is a vecto quantity. The SI unit of momentum is kg m s 1. Newton's second law defines foce as the ate of change of momentum ( mv) F =. t If the mass is constant this can be expessed as 'foce = mass acceleation' because acceleation is ate of change of velocity. The change of momentum of an object acted on by a foce is: ( mv) = F t. The poduct F t is called the impulse of the foce. The thust on a ocket of the jet of gases that it ejects is equal to the ate at which the jet caies away momentum. This is given by the mass ejected pe second x the velocity of the jet. When two objects inteact, fo example in a collision, one object loses an amount of momentum and the othe object gains an equal amount. The total momentum of the two objects is the same afte the inteaction as befoe. This is the pinciple of consevation of momentum. Since the time of inteaction t is the same fo both objects, the foces acting on the objects ae equal and opposite. This is Newton s Thid Law. It is a consequence of the consevation of momentum. Newton's laws of motion Newton's fist law of motion states that an object emains at est o moves with constant velocity unless acted on by a esultant foce. Newton's fist law defines what a foce is, namely any physical effect that is capable of changing the motion of an object. If an object is at est o in unifom motion, eithe no foce acts on it o foces do act on it and the esultant foce is zeo. Newton's second law of motion states that the ate of change of momentum of an object is equal to the esultant foce on the object. That is, F = dp / dt, whee p = mv is the momentum of an object acted on by a esultant foce F. Fo an object of constant mass m, acted on by a foce F dv F = m = ma dt Advancing Physics A 4

5 The SI unit of foce is the newton (N). 1 N is the foce that gives a 1 kg mass an acceleation of 1 m s. Newton's thid law of motion states that when two objects inteact, thee is an equal and opposite foce on each. Gavitational field The stength g of a gavitational field at a point is the gavitational foce pe unit mass acting on a small mass at that point. Gavitational field stength is a vecto quantity in the diection of the gavitational foce. The SI unit of gavitational field stength is N kg -1 o equivalently m s -. The foce F on a point mass m at a point in a gavitational field is given by F = m g, whee g is the gavitational field stength at that point. Close to the suface of the Eath, the gavitational field is almost unifom. The lines of foce ae paallel and at ight angles to the Eath's suface. A unifom gavitational field unifom field ove distance << adius R spheical planet of adius R adial field On a lage scale, the gavitational field is adial. Newton's law of gavitation states that the foce of gavitational attaction F of a mass M on anothe mass m obeys an invese squae law: GMm F = whee is the distance fom the cente of M to m and the minus sign indicates that the foce acts towads the mass M. The measued value of the Univesal Gavitational Constant G is N m kg -. The gavitational field stength g = F / m = G M / at distance fom the cente of the mass M. Advancing Physics A 5

6 Vaiation of g with distance fom the cente of the Eath distance fom cente adius of Eath Gavitational potential The gavitational potential at a point is the potential enegy pe unit mass of a small object placed at that point. This is the wok done pe unit mass to move a small object fom infinity to that point. The gavitational potential enegy E P of a point mass m is given by E P = m V G, whee V G is the gavitational potential at that point. The SI unit of gavitational potential is J kg 1. Gavitational potential is a scala quantity. An equipotential is a suface of constant potential. No change of potential enegy occus when an object is moved along an equipotential. The lines of foce ae theefoe always pependicula to the equipotential sufaces. The gavitational field stength at a point in a gavitational field is the negative of the potential gadient at that point. In symbols g = dv G / dx. In an invese squae gavitational field, the field stength is: GM g =. and the gavitational potential is: GM V G = Advancing Physics A 6

7 Vaiation of gavitational potential with distance fom the cente of a spheical body 0 distance fom cente / adius of body Vs Vs suface potential Motion in a cicle An object moving in a hoizontal cicle at constant speed changes its diection of motion continuously. Its velocity is not constant because its diection of motion is not constant. The esultant foce is diected towads the cente of the cicle. It is called the centipetal foce. Fo an object moving at constant speed v along a cicula path of adius, the acceleation towads the cente is: v a = and the centipetal foce F acting on it is: mv F = ma = whee m is the mass of the object. The centipetal foce does no wok on the moving mass because the foce is always at ight angles to the diection of motion. The enegy of the motion is theefoe constant. The time T taken to move once ound the cicula path is T = π / v Fo a poof that v a = see Summay diagams: Centipetal acceleation Advancing Physics A 7

8 Summay Diagams (OHTs) Back to list of Contents Consevation of momentum Consevation of momentum p = mv Befoe collision: p 1 p [total momentum p] befoe = [m 1 v 1 + m v ] befoe m 1 m Afte collision: p 1 p [total momentum p] afte = [m 1 v 1 + m v ] afte Duing collision: momentum p goes fom one mass to the othe befoe: Momentum conseved loses p p 1 p p p [p 1 ] afte = [p 1 ] befoe p [p ] afte = [p ] befoe + p [ p] total = 0 gains p afte: p 1 p theefoe: [p 1 + p ] afte = [p 1 + p ] befoe Changes of velocity: m 1 v 1 = p m v = + p theefoe: v v 1 = m 1 m changes of momentum ae equal and opposite changes of velocity ae in invese popotion to mass Momentum just goes fom one object to the othe. The total momentum is constant Advancing Physics A 8

9 Collisions fom diffeent viewpoints Two equally massive spacecaft dock togethe and join. The collision is seen fom two diffeent moving points of view. Momentum is conseved fom both points of view Two cafts appoach one anothe and dock togethe View 1 Obsevation caft hoves whee the caft will meet +v v Pogess Mi obsevation caft video of collision seen fom obsevation caft +v v Pogess Mi View Obsevation caft tavels alongside Mi +v v Pogess Mi v obsevation caft video of collision seen fom obsevation caft +v +v Pogess Mi The same event looks diffeent fom two diffeent points of view Advancing Physics A 9

10 One event seen fom two points of view Befoe collision +v v Pogess Mi momentum befoe = +mv mv = 0 Afte collision velocity = 0 Pogess Mi momentum afte = 0 Befoe collision velocity of this fame elative to fame above velocity = 0 +v Pogess Mi Afte collision momentum befoe = +m(v) = +mv m +v Pogess Mi momentum afte = (m)v = mv Momentum is diffeent in the two views of the same event, but in each case: momentum afte = momentum befoe Advancing Physics A 10

11 Examples of collisions Hee ae six collisions. Notice that the total momentum befoe is always equal to the total momentum afte. equal masses, inelastic collision befoe velocity v velocity v total momentum befoe 0 duing afte both velocities zeo afte 0 equal masses, elastic collision befoe total momentum velocity v velocity zeo befoe duing afte afte velocity zeo velocity v equal masses, elastic collision befoe velocity v velocity v total momentum befoe 0 duing afte velocity v velocity v afte 0 Advancing Physics A 11

12 unequal masses, inelastic collision befoe total momentum velocity v velocity zeo befoe duing afte velocity a little less than v afte unequal masses, elastic collision befoe total momentum velocity v velocity zeo befoe duing afte velocity a little less than v velocity much less than v afte unequal masses, elastic collision befoe total momentum velocity v velocity zeo befoe duing afte velocity much less than v velocity up to v afte Advancing Physics A 1

13 Momentum and foce Thinking about momentum and foces Pinciple 1 symmety +v v identical objects esult pedictable fom symmety Pinciple invaiance +v v seen diffeently is the same as: +v Consevation of momentum p + p cunch p mass M foce F acts fo time t change of momentum = F t Split cunch into foces F on each foce F = p t same time t. foces equal and opposite foce +F acts fo time t mass m + p change of momentum = F t if define foce F = p t then F = m v = ma t thus F = ma Fom symmety and invaiance (looking diffeently can t change events): 1. momentum is conseved. define mass fom change of velocity in collision 3. define foce as ate of change of momentum, giving F = ma 4. foces on inteacting objects act in equal and opposite pais Advancing Physics A 13

14 Jets and ockets Jets and ockets momentum caied by gas plus momentum change of ocket = 0 ocket velocity V inceases by V in time t p momentum caied away by jet: p = v m in time t ocket mass M p change of momentum of ocket: p = M V in time t mass m ejected in time t fo jet: v m = p equal and opposite fo ocket: p = M V M V = v m V = v m M gas velocity v thust = p = M V v m = t t t Advancing Physics A 14

15 Field diection and equipotentials Gavitational gadients aound Eath Equipotentials ae sphees contou of constant gavitational potential gavitational field Advancing Physics A 15

16 Centipetal acceleation Acceleation towads cente of cicula obit cicula path adius speed v A B v 1 v θ velocity tuns though angle θ as planet goes along cicula path in shot time t adius tuns though θ velocity tuns though θ A speed v θ v 1 B v v θ θ = ac AB ac AB = distance in time t at speed v ac AB = v t change of velocity v towads cente of cicle v t = θ θ v v v t v v multiply by v: v v t divide by t: v = = v v t = acceleation Acceleation towads cente = v Advancing Physics A 16

17 Keple: Geomety ules the Univese Law 1: a planet moves in an ellipse with the Sun at one focus Astonomy Mas Geomety planet a b Sun focus focus Obit of Mas an ellipse with Sun at a focus Ellipse: cuve such that sum of a and b is constant Keple: Geomety ules the Univese Law : the line fom the Sun to a planet sweeps out equal aeas in equal times Astonomy Mas Geomety planet fast Sun slow focus Speed of planet lage nea Sun, smalle away fom Sun Aeas swept out in same time ae equal Advancing Physics A 17

18 Keple: Geomety ules the Univese Law 3: squae of obital time is popotional to cube of obital adius Obital peiod against obital adius Mas 4 3 Obital peiod squaed against obital adius cubed Mas 1 Eath Venus 1 Eath Mecuy adius/million km Venus 0 Mecuy adius 3 /AU 3 Advancing Physics A 18

19 Satellites and Keple s thid law The example of a geostationay satellite is used to deive Keple s thid law. Geostationay satellite m = mass of satellite R = adius of satellite obit v = speed in obit G = gavitational constant = N kg m M = mass of Eath = kg T = time of obit = 4 hous = s N obit adius R = 4000 km gavitational foce S satellite obit tuns at same ate as Eath tuns Calculating the adius of obit Foce poducing acceleation to cente mv R equal Gavitational foce on satellite GMm R Foces ae equal: mv R divide by m: v R = = GMm R GM R speed in obit depends on time of obit and adius v = πr T multiply by R: v = GM R equal v 4π R = T equate expessions fo v : GM R 4π R T eaange to calculate R: GMT 4π = R 3 = Keple s thid law deduced inset values of G, M and T: R = km R = 6.6 adius of Eath (6400 km) Advancing Physics A 19

FXA 2008. Candidates should be able to : Describe how a mass creates a gravitational field in the space around it.

FXA 2008. Candidates should be able to : Describe how a mass creates a gravitational field in the space around it. Candidates should be able to : Descibe how a mass ceates a gavitational field in the space aound it. Define gavitational field stength as foce pe unit mass. Define and use the peiod of an object descibing

More information

mv2. Equating the two gives 4! 2. The angular velocity is the angle swept per GM (2! )2 4! 2 " 2 = GM . Combining the results we get !

mv2. Equating the two gives 4! 2. The angular velocity is the angle swept per GM (2! )2 4! 2  2 = GM . Combining the results we get ! Chapte. he net foce on the satellite is F = G Mm and this plays the ole of the centipetal foce on the satellite i.e. mv mv. Equating the two gives = G Mm i.e. v = G M. Fo cicula motion we have that v =!

More information

Chapter 5: Circular Motion : Earlier in the semester. Universal Law of Gravitation: Today. Newton s Universal Law of Gravitation

Chapter 5: Circular Motion : Earlier in the semester. Universal Law of Gravitation: Today. Newton s Universal Law of Gravitation Chapte 5: Cicula otion : Ealie in the semeste Univesal Law of Gavitation: Today 1 Newton s Univesal Law of Gavitation 1 Newton s Law of Univesal Gavitation Fo a pai of point masses Diection: towads each

More information

Chapter 13 Gravitation. Problems: 1, 4, 5, 7, 18, 19, 25, 29, 31, 33, 43

Chapter 13 Gravitation. Problems: 1, 4, 5, 7, 18, 19, 25, 29, 31, 33, 43 Chapte 13 Gavitation Poblems: 1, 4, 5, 7, 18, 19, 5, 9, 31, 33, 43 Evey object in the univese attacts evey othe object. This is called gavitation. We e use to dealing with falling bodies nea the Eath.

More information

Physics 235 Chapter 5. Chapter 5 Gravitation

Physics 235 Chapter 5. Chapter 5 Gravitation Chapte 5 Gavitation In this Chapte we will eview the popeties of the gavitational foce. The gavitational foce has been discussed in geat detail in you intoductoy physics couses, and we will pimaily focus

More information

Gravitation. AP Physics C

Gravitation. AP Physics C Gavitation AP Physics C Newton s Law of Gavitation What causes YOU to be pulled down? THE EARTH.o moe specifically the EARTH S MASS. Anything that has MASS has a gavitational pull towads it. F α Mm g What

More information

Chapter 13 Gravitation

Chapter 13 Gravitation Chapte 13 Gavitation Newton, who extended the concept of inetia to all bodies, ealized that the moon is acceleating and is theefoe subject to a centipetal foce. He guessed that the foce that keeps the

More information

Section 39 Gravitational Potential Energy & General Relativity

Section 39 Gravitational Potential Energy & General Relativity Section 39 Gavitational Potential Enegy & Geneal elativity What is the univese made out of and how do the pats inteact? We ve leaned that objects do what they do because of foces, enegy, linea and angula

More information

Universal Gravitation

Universal Gravitation J - The Foce of Gavity Chapte J Univesal Gavitation Blinn College - Physics 45 - Tey Honan Intoduction If Isaac Newton had meely witten down his thee laws of motion he would pobably still be known as the

More information

Newton s Law of Universal Gravitation Every object in the universe is attracted to every other object. r 2

Newton s Law of Universal Gravitation Every object in the universe is attracted to every other object. r 2 6//01 Newton s Law of Univesal Gavitation Evey object in the univese is attacted to evey othe object. Cavendish poves the law in 1798 F= Gm 1 m G = 6.67 X 10-11 N-m /kg m 1 = mass of one object m = mass

More information

jfpr% ekuo /kez iz.ksrk ln~xq# Jh j.knksm+nklth egkjkt

jfpr% ekuo /kez iz.ksrk ln~xq# Jh j.knksm+nklth egkjkt Phone : 0 903 903 7779, 98930 58881 Gavitation Page: 8 fo/u fopkj Hkh# tu] ugha vkjehks dke] foif ns[k NksM+s qja e/;e eu dj ';kea iq#"k flag ladyi dj] lgs foif vusd] ^cuk^ u NksM+s /;s; dks] j?kqcj jk[ks

More information

Lecture 19: Effective Potential, and Gravity

Lecture 19: Effective Potential, and Gravity Lectue 19: Effective Potential, and Gavity The expession fo the enegy of cental-foce motion was: 1 ( ) l E = µ + U + µ We can teat this as a one-dimensional poblem if we define an effective potential:

More information

GRAVITATIONAL FIELD: CHAPTER 11. The groundwork for Newton s great contribution to understanding gravity was laid by three majors players:

GRAVITATIONAL FIELD: CHAPTER 11. The groundwork for Newton s great contribution to understanding gravity was laid by three majors players: CHAPT 11 TH GAVITATIONAL FILD (GAVITY) GAVITATIONAL FILD: The goundwok fo Newton s geat contibution to undestanding gavity was laid by thee majos playes: Newton s Law of Gavitation o gavitational and inetial

More information

Exam 3: Equation Summary

Exam 3: Equation Summary MASSACHUSETTS INSTITUTE OF TECHNOLOGY Depatment of Physics Physics 8.1 TEAL Fall Tem 4 Momentum: p = mv, F t = p, Fext ave t= t f t= Exam 3: Equation Summay total = Impulse: I F( t ) = p Toque: τ = S S,P

More information

12. Rolling, Torque, and Angular Momentum

12. Rolling, Torque, and Angular Momentum 12. olling, Toque, and Angula Momentum 1 olling Motion: A motion that is a combination of otational and tanslational motion, e.g. a wheel olling down the oad. Will only conside olling with out slipping.

More information

The Role of Gravity in Orbital Motion

The Role of Gravity in Orbital Motion ! The Role of Gavity in Obital Motion Pat of: Inquiy Science with Datmouth Developed by: Chistophe Caoll, Depatment of Physics & Astonomy, Datmouth College Adapted fom: How Gavity Affects Obits (Ohio State

More information

F G r. Don't confuse G with g: "Big G" and "little g" are totally different things.

F G r. Don't confuse G with g: Big G and little g are totally different things. G-1 Gavity Newton's Univesal Law of Gavitation (fist stated by Newton): any two masses m 1 and m exet an attactive gavitational foce on each othe accoding to m m G 1 This applies to all masses, not just

More information

Resources. Circular Motion: From Motor Racing to Satellites. Uniform Circular Motion. Sir Isaac Newton 3/24/10. Dr Jeff McCallum School of Physics

Resources. Circular Motion: From Motor Racing to Satellites. Uniform Circular Motion. Sir Isaac Newton 3/24/10. Dr Jeff McCallum School of Physics 3/4/0 Resouces Cicula Motion: Fom Moto Racing to Satellites D Jeff McCallum School of Physics http://www.gap-system.og/~histoy/mathematicians/ Newton.html http://www.fg-a.com http://www.clke.com/clipat

More information

2 r2 θ = r2 t. (3.59) The equal area law is the statement that the term in parentheses,

2 r2 θ = r2 t. (3.59) The equal area law is the statement that the term in parentheses, 3.4. KEPLER S LAWS 145 3.4 Keple s laws You ae familia with the idea that one can solve some mechanics poblems using only consevation of enegy and (linea) momentum. Thus, some of what we see as objects

More information

8-1 Newton s Law of Universal Gravitation

8-1 Newton s Law of Universal Gravitation 8-1 Newton s Law of Univesal Gavitation One of the most famous stoies of all time is the stoy of Isaac Newton sitting unde an apple tee and being hit on the head by a falling apple. It was this event,

More information

PHYSICS 111 HOMEWORK SOLUTION #13. May 1, 2013

PHYSICS 111 HOMEWORK SOLUTION #13. May 1, 2013 PHYSICS 111 HOMEWORK SOLUTION #13 May 1, 2013 0.1 In intoductoy physics laboatoies, a typical Cavendish balance fo measuing the gavitational constant G uses lead sphees with masses of 2.10 kg and 21.0

More information

14. Gravitation Universal Law of Gravitation (Newton):

14. Gravitation Universal Law of Gravitation (Newton): 14. Gavitation 1 Univesal Law of Gavitation (ewton): The attactive foce between two paticles: F = G m 1m 2 2 whee G = 6.67 10 11 m 2 / kg 2 is the univesal gavitational constant. F m 2 m 1 F Paticle #1

More information

Gravity. Physics 6B. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

Gravity. Physics 6B. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Gavity Physics 6B Pepaed by Vince Zaccone o Capus Leaning Assistance Sevices at UCSB GRAVITY Any pai of objects, anywhee in the univese, feel a utual attaction due to gavity. Thee ae no exceptions if you

More information

Gravitation and Kepler s Laws Newton s Law of Universal Gravitation in vectorial. Gm 1 m 2. r 2

Gravitation and Kepler s Laws Newton s Law of Universal Gravitation in vectorial. Gm 1 m 2. r 2 F Gm Gavitation and Keple s Laws Newton s Law of Univesal Gavitation in vectoial fom: F 12 21 Gm 1 m 2 12 2 ˆ 12 whee the hat (ˆ) denotes a unit vecto as usual. Gavity obeys the supeposition pinciple,

More information

Chapter 25 Electric Potential

Chapter 25 Electric Potential Chapte 5 Electic Potential Can we apply the concept of potential, fist intoduced in mechanics, to electostatic system and find the law of consevation of enegy? We can define an electostatic potential enegy,

More information

General Physics (PHY 2130)

General Physics (PHY 2130) Geneal Physics (PHY 130) Lectue 1 Rotational kinematics Angula speed and acceleation Unifom and non-unifom cicula motion Obits and Keple s laws http://www.physics.wayne.edu/~apeto/phy130/ Lightning Reiew

More information

Episode 401: Newton s law of universal gravitation

Episode 401: Newton s law of universal gravitation Episode 401: Newton s law of univesal gavitation This episode intoduces Newton s law of univesal gavitation fo point masses, and fo spheical masses, and gets students pactising calculations of the foce

More information

19.1 Potential Energy

19.1 Potential Energy Chapte 19: Electic Potential Enegy & Electic Potential Why electic field contains enegy? Is thee an altenative way to undestand electic field? Concepts: Wok done by consevative foce Electic potential enegy

More information

Lab 5: Circular Motion

Lab 5: Circular Motion Lab 5: Cicula motion Physics 193 Fall 2006 Lab 5: Cicula Motion I. Intoduction The lab today involves the analysis of objects that ae moving in a cicle. Newton s second law as applied to cicula motion

More information

PHYS-2010: General Physics I Course Lecture Notes Section IX

PHYS-2010: General Physics I Course Lecture Notes Section IX PHYS-200: Geneal Physics I Couse Lectue Notes Section IX D. Donald G. Luttemose East Tennessee State Univesity Edition 2.5 Abstact These class notes ae designed fo use of the instucto and students of the

More information

DO PHYSICS ONLINE GRAVITATIONAL FIEDS

DO PHYSICS ONLINE GRAVITATIONAL FIEDS DO PHYSICS ONLIN SPAC GRAVITATIONAL FIDS NWTON S LAW OF UNIVRSAL GRAVITATION Newton's Univesal Law of Gavitation states that any two objects exet a gavitational foce of attaction on each othe. The diection

More information

Newton s Law of Gravity and Orbits of Planets & Satellites

Newton s Law of Gravity and Orbits of Planets & Satellites he Uniesal Law of Gaitation Newton s Law of Gaity and Obits of Planets & Satellites Newton s Uniesal Law of Gaitation states that any two point asses attact each othe with a foce popotional to the poduct

More information

Explosions and collisions obey some surprisingly simple laws that make problem solving easier when comparing the situation before and after an

Explosions and collisions obey some surprisingly simple laws that make problem solving easier when comparing the situation before and after an Chapte 9. Impulse and Momentum Explosions and collisions obey some supisingly simple laws that make poblem solving easie when compaing the situation befoe and afte an inteaction. Chapte Goal: To intoduce

More information

A) 2 B) 2 C) 2 2 D) 4 E) 8

A) 2 B) 2 C) 2 2 D) 4 E) 8 Page 1 of 8 CTGavity-1. m M Two spheical masses m and M ae a distance apat. The distance between thei centes is halved (deceased by a facto of 2). What happens to the magnitude of the foce of gavity between

More information

Brown University PHYS 0060 ELECTRIC POTENTIAL

Brown University PHYS 0060 ELECTRIC POTENTIAL INTRODUCTION ELECTRIC POTENTIL You have no doubt noticed that TV sets, light bulbs, and othe electic appliances opeate on 115 V, but electic ovens and clothes dyes usually need 220 V. atteies may be ated

More information

Recap: Newton s Gravitational Law

Recap: Newton s Gravitational Law Recap: Newton s Gavitational Law The gavitational foce between two objects is popotional to thei masses and invesely popotional to the squae of the distance between thei centes. F = G m 1 m (Newtons) F

More information

Version 001 Review 4 Electric Force, Magnetic fields tubman (19112) 1

Version 001 Review 4 Electric Force, Magnetic fields tubman (19112) 1 Vesion 001 Review 4 Electic Foce, Magnetic fields tubman (19112) 1 This pint-out should have 42 questions. Multiple-choice questions may continue on the next column o page find all choices befoe answeing.

More information

Gravitational Field and its Potential

Gravitational Field and its Potential Lectue 19 Monday - Octobe 17, 2005 Witten o last updated: Octobe 17, 2005 P441 Analytical Mechanics - I Gavitational Field and its Potential c Alex. Dzieba Isaac Newton What Isaac Newton achieved was tuly

More information

Magnetic Fields. Ch.28: The magnetic field: Lorentz Force Law Ch.29: Electromagnetism: Ampere s Law HOMEWORK

Magnetic Fields. Ch.28: The magnetic field: Lorentz Force Law Ch.29: Electromagnetism: Ampere s Law HOMEWORK Magnetic Fields Ch.28: The magnetic field: Loentz Foce Law Ch.29: Electomagnetism: Ampee s Law HOMEWORK Read Chaptes 28 and 29 Do Chapte 28 Questions 1, 7 Do Chapte 28 Poblems 3, 15, 33, 47 Today The Magnetic

More information

Chapter 5. Dynamics of Uniform Circular Motion

Chapter 5. Dynamics of Uniform Circular Motion Chapte 5 Dynamics of Unifom Cicula Motion 5.1 Unifom Cicula Motion DEFINITION OF UNIFORM CIRCULAR MOTION Unifom cicula motion is the motion of an object taveling at a constant speed on a cicula path. 5.1

More information

Ch. 8 Universal Gravitation. Part 1: Kepler s Laws. Johannes Kepler. Tycho Brahe. Brahe. Objectives: Section 8.1 Motion in the Heavens and on Earth

Ch. 8 Universal Gravitation. Part 1: Kepler s Laws. Johannes Kepler. Tycho Brahe. Brahe. Objectives: Section 8.1 Motion in the Heavens and on Earth Ch. 8 Univesal Gavitation Pat 1: Keple s Laws Objectives: Section 8.1 Motion in the Heavens and on Eath Objectives Relate Keple s laws of planetay motion to Newton s law of univesal gavitation. Calculate

More information

Voltage ( = Electric Potential )

Voltage ( = Electric Potential ) V-1 of 9 Voltage ( = lectic Potential ) An electic chage altes the space aound it. Thoughout the space aound evey chage is a vecto thing called the electic field. Also filling the space aound evey chage

More information

Lecture 4. Home Exercise: Welcome to Wisconsin

Lecture 4. Home Exercise: Welcome to Wisconsin Lectue 4 ltoday: h. 3 (all) & h. 4 (stat) v Pefom vecto algeba (addition and subtaction) v Inteconvet between atesian and Pola coodinates v Wok with D motion Deconstuct motion into x & y o paallel & pependicula

More information

General Physics (PHY 2130)

General Physics (PHY 2130) Geneal Physics (PHY 130) Lectue 13 Rotational kinematics Non-unifom cicula motion Obits and Keple s laws http://www.physics.wayne.edu/~apeto/phy130/ Lightning Reiew Last lectue: 1. Rotational kinematics

More information

PY1052 Problem Set 3 Autumn 2004 Solutions

PY1052 Problem Set 3 Autumn 2004 Solutions PY1052 Poblem Set 3 Autumn 2004 Solutions C F = 8 N F = 25 N 1 2 A A (1) A foce F 1 = 8 N is exeted hoizontally on block A, which has a mass of 4.5 kg. The coefficient of static fiction between A and the

More information

The Effects of Moons on Saturn s Ring System

The Effects of Moons on Saturn s Ring System The Effects of Moons on Satun s Ring System Kisten Lason Physics Depatment, The College of Wooste, Wooste, Ohio 44691, USA (Dated: May 10, 007) The ing system of Satun is a complex inteaction between numeous

More information

Laws of Motion; Circular Motion

Laws of Motion; Circular Motion Pactice Test: This test coves Newton s Laws of Motion, foces, coefficients of fiction, fee-body diagams, and centipetal foce. Pat I. Multiple Choice 3m 2m m Engine C B A 1. A locomotive engine of unknown

More information

Physics E1ax Solutions: Assignment for Feb. 3 Feb. 10 Homework #1: Electric Potential, Coulomb s Law, Equipotentials

Physics E1ax Solutions: Assignment for Feb. 3 Feb. 10 Homework #1: Electric Potential, Coulomb s Law, Equipotentials Physics Eax Solutions: Assignment fo Feb. 3 Feb. 0 Homewok #: Electic Potential, Coulomb s Law, Equipotentials Afte completing this homewok assignment, you should be able to Undestand the diffeence between

More information

Determining solar characteristics using planetary data

Determining solar characteristics using planetary data Detemining sola chaacteistics using planetay data Intoduction The Sun is a G type main sequence sta at the cente of the Sola System aound which the planets, including ou Eath, obit. In this inestigation

More information

6.2. orbits. Satellites and Space Stations

6.2. orbits. Satellites and Space Stations obits RADARSAT-1 and RADARSAT-2 ae Eath-obsevation satellites designed and commissioned by the Canadian Space Agency. These eyes in the skies pee down fom obit, captuing images and data that help scientists

More information

CHAPTER 5 DYNAMIC OF UNIFORM CIRCULAR MOTION

CHAPTER 5 DYNAMIC OF UNIFORM CIRCULAR MOTION CHAPER 5 DYAMIC OF UIFORM CIRCULAR MOIO 5.1 UIFORM CIRCULAR MOIO: Unifom cicula motion is the motion of an object taeling at a constant o unifom speed on a cicula path. If the peiod is the time equied

More information

Samples of conceptual and analytical/numerical questions from chap 21, C&J, 7E

Samples of conceptual and analytical/numerical questions from chap 21, C&J, 7E CHAPTER 1 Magnetism CONCEPTUAL QUESTIONS Cutnell & Johnson 7E 3. ssm A chaged paticle, passing though a cetain egion of space, has a velocity whose magnitude and diection emain constant, (a) If it is known

More information

Multiple choice questions [60 points]

Multiple choice questions [60 points] 1 Multiple choice questions [60 points] Answe all o the ollowing questions. Read each question caeully. Fill the coect bubble on you scanton sheet. Each question has exactly one coect answe. All questions

More information

Working with Gravity: Potential Energy

Working with Gravity: Potential Energy pevious index next Woking with Gavity: Potential negy Michael Fowle 31/1/07 Gavitational Potential negy nea the ath We fist biefly eview the familia subject of gavitational potential enegy nea the ath

More information

Assessment Schedule 2014 Physics: Demonstrate understanding of mechanical systems (91524)

Assessment Schedule 2014 Physics: Demonstrate understanding of mechanical systems (91524) NCEA Level 3 Physics (91524) 2014 page 1 of 9 Assessment Schedule 2014 Physics: Demonstate undestanding of mechanical systems (91524) Assessment Citeia Achievement Achievement with Meit Achievement with

More information

Chapter 10. Dynamics of Rotational Motion

Chapter 10. Dynamics of Rotational Motion 10.1 Toque Chapte 10 Dynamics of Rotational Motion The wod toque comes fom the Latin wod that means twist. The toque! of a foce F about a point P in space is equal to the coss poduct (also called vecto

More information

Phys 170 Practice Final 2 Solutions. . The denominator is The application points are B r. = ( 1.5,+1.5,0). The load force is 3.

Phys 170 Practice Final 2 Solutions. . The denominator is The application points are B r. = ( 1.5,+1.5,0). The load force is 3. Phys 170 Pactice Final 2 Solutions 1. The massless semicicula plate with adius 1.5 m is suppoted by cables D and CD and a ball and socket joint A, and a load of 300 N is applied at the point shown. Find

More information

2008 Quarter-Final Exam Solutions

2008 Quarter-Final Exam Solutions 2008 Quate-final Exam - Solutions 1 2008 Quate-Final Exam Solutions 1 A chaged paticle with chage q and mass m stats with an initial kinetic enegy K at the middle of a unifomly chaged spheical egion of

More information

Electric & Potential Fields

Electric & Potential Fields Electic & Potential Fields Pupose An electic field suounds any assemblage of chaged objects. To detemine the stength and diection of these fields, it is most convenient to fist map the electic potential

More information

PY1052 Problem Set 8 Autumn 2004 Solutions

PY1052 Problem Set 8 Autumn 2004 Solutions PY052 Poblem Set 8 Autumn 2004 Solutions H h () A solid ball stats fom est at the uppe end of the tack shown and olls without slipping until it olls off the ight-hand end. If H 6.0 m and h 2.0 m, what

More information

Chapter 13. Vector-Valued Functions and Motion in Space 13.6. Velocity and Acceleration in Polar Coordinates

Chapter 13. Vector-Valued Functions and Motion in Space 13.6. Velocity and Acceleration in Polar Coordinates 13.6 Velocity and Acceleation in Pola Coodinates 1 Chapte 13. Vecto-Valued Functions and Motion in Space 13.6. Velocity and Acceleation in Pola Coodinates Definition. When a paticle P(, θ) moves along

More information

1.1 KINEMATIC RELATIONSHIPS

1.1 KINEMATIC RELATIONSHIPS 1.1 KINEMATIC RELATIONSHIPS Thoughout the Advanced Highe Physics couse calculus techniques will be used. These techniques ae vey poweful and knowledge of integation and diffeentiation will allow a deepe

More information

Chapter 26 - Electric Field. A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University

Chapter 26 - Electric Field. A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University Chapte 6 lectic Field A PowePoint Pesentation by Paul. Tippens, Pofesso of Physics Southen Polytechnic State Univesity 7 Objectives: Afte finishing this unit you should be able to: Define the electic field

More information

Gauss's Law. EAcos (for E = constant, surface flat ) 1 of 11

Gauss's Law. EAcos (for E = constant, surface flat ) 1 of 11 1 of 11 Gauss's Law Gauss's Law is one of the 4 funmental laws of electicity and magnetism called Maxwell's quations. Gauss's law elates chages and electic fields in a subtle and poweful way, but befoe

More information

3 The Electric Field Due to one or more Point Charges

3 The Electric Field Due to one or more Point Charges Chapte 3 The lectic Field Due to one o moe Point Chages 3 The lectic Field Due to one o moe Point Chages A chaged paticle (a.k.a. a point chage, a.k.a. a souce chage) causes an electic field to exist in

More information

Problem Set 5: Universal Law of Gravitation; Circular Planetary Orbits.

Problem Set 5: Universal Law of Gravitation; Circular Planetary Orbits. MASSACHUSETTS INSTITUTE OF TECHNOLOGY Depatment of Physics Physics 8.01T Fall Tem 2004 Poblem Set 5: Univesal Law of Gavitation; Cicula Planetay Obits. Available on-line Octobe 1; Due: Octobe 12 at 4:00

More information

Uniform Circular Motion. Banked and Unbanked Curves Circular Orbits Nonuniform Circular Motion Tangential and Angular Acceleration Artificial Gravity

Uniform Circular Motion. Banked and Unbanked Curves Circular Orbits Nonuniform Circular Motion Tangential and Angular Acceleration Artificial Gravity Chapte 5: Cicula Motion Unifom Cicula Motion Radial Acceleation Banked and Unbanked Cues Cicula Obits Nonunifom Cicula Motion Tangential and Angula Acceleation Atificial Gaity 1 Unifom Cicula Motion y

More information

Problem Set 6: Solutions

Problem Set 6: Solutions UNIVESITY OF ALABAMA Depatment of Physics and Astonomy PH 16-4 / LeClai Fall 28 Poblem Set 6: Solutions 1. Seway 29.55 Potons having a kinetic enegy of 5. MeV ae moving in the positive x diection and ente

More information

A2 Physics. Unit 5. Unit 4. Fields and Further Mechanics. Nuclear and Thermal Physics. 1 Momentum and Collisions. 1 Rutherford Scattering

A2 Physics. Unit 5. Unit 4. Fields and Further Mechanics. Nuclear and Thermal Physics. 1 Momentum and Collisions. 1 Rutherford Scattering A Physics Unit 4 Fields and Futhe Mechanics Momentum and Collisions Foce and Impulse Cicula Motion 4 Centipetal Foce and Acceleation 5 Simple Hamonic Motion 6 SHM Gaphs 7 SHM Time Peiods 8 Resonance and

More information

1. Circular Motion. Explain the terms: Radius vector, Angular displacement (θ) angular velocity ( ) angular acceleration ( )

1. Circular Motion. Explain the terms: Radius vector, Angular displacement (θ) angular velocity ( ) angular acceleration ( ) 1. Cicula Motion SAPTAS HI What is Cicula motion? Give example. Motion of an object along cicumfeence of a cicle is called cicula motion. E.g. Motion of eath ound the sun is appoximately cicula. Electons

More information

Chapter 23: Gauss s Law

Chapter 23: Gauss s Law Chapte 3: Gauss s Law Homewok: Read Chapte 3 Questions, 5, 1 Poblems 1, 5, 3 Gauss s Law Gauss s Law is the fist of the fou Maxwell Equations which summaize all of electomagnetic theoy. Gauss s Law gives

More information

Sources of the Magnetic Field. Physics 231 Lecture 8-1

Sources of the Magnetic Field. Physics 231 Lecture 8-1 Souces of the Magnetic Field Physics 31 Lectue 8-1 Magnetic Field of a Point Chage Given a point chage, q, we know that it geneates an electic field egadless of whethe it is moving o not f the chage is

More information

Physics 202, Lecture 4. Gauss s Law: Review

Physics 202, Lecture 4. Gauss s Law: Review Physics 202, Lectue 4 Today s Topics Review: Gauss s Law Electic Potential (Ch. 25-Pat I) Electic Potential Enegy and Electic Potential Electic Potential and Electic Field Next Tuesday: Electic Potential

More information

ESCAPE VELOCITY EXAMPLES

ESCAPE VELOCITY EXAMPLES ESCAPE VELOCITY EXAMPLES 1. Escape velocity is the speed that an object needs to be taveling to beak fee of planet o moon's gavity and ente obit. Fo example, a spacecaft leaving the suface of Eath needs

More information

Voltage ( = Electric Potential )

Voltage ( = Electric Potential ) V-1 Voltage ( = Electic Potential ) An electic chage altes the space aound it. Thoughout the space aound evey chage is a vecto thing called the electic field. Also filling the space aound evey chage is

More information

Displacement, Velocity And Acceleration

Displacement, Velocity And Acceleration Displacement, Velocity And Acceleation Vectos and Scalas Position Vectos Displacement Speed and Velocity Acceleation Complete Motion Diagams Outline Scala vs. Vecto Scalas vs. vectos Scala : a eal numbe,

More information

Pre-lab Quiz/PHYS 224 Earth s Magnetic Field. Your name Lab section

Pre-lab Quiz/PHYS 224 Earth s Magnetic Field. Your name Lab section Pe-lab Quiz/PHYS 224 Eath s Magnetic Field You name Lab section. What do you investigate in this lab? 2. Fo a pai of Helmholtz coils descibed in this manual and shown in Figue 2, =.5 m, N = 3, I =.4 A,

More information

Chapter 13. Universal Gravitation

Chapter 13. Universal Gravitation Chapte 13 Univesal Gavitation CHAPTER OUTLINE 13.1 Newton s Law of Univesal Gavitation 13.2 Measuing the Gavitational Constant 13.3 Fee-Fall Acceleation and the Gavitational Foce 13.4 Keple s Laws and

More information

CHAPTER 21 CENTRAL FORCES AND EQUIVALENT POTENTIAL

CHAPTER 21 CENTRAL FORCES AND EQUIVALENT POTENTIAL 1 1.1 Intoduction CHAPTER 1 CENTRA FORCES AND EQUIVAENT POTENTIA Wen a paticle is in obit aound a point unde te influence of a cental attactive foce (i.e. a foce F () wic is diected towads a cental point,

More information

Right Hand Rule. Magnetic field is defined in terms of the force on a moving charge. B=F/qvsinΘ for a moving charge or F=qvxB.

Right Hand Rule. Magnetic field is defined in terms of the force on a moving charge. B=F/qvsinΘ for a moving charge or F=qvxB. Magnetic field is defined in tems of the foce on a moving chage =/qvsinθ fo a moving chage o =qvx =/lsinθ o =lx fo a cuent Right Hand Rule Hold you ight hand open Place you finges in the diection of Place

More information

Lecture 8.1 Gravitation 1. Gravitational Force

Lecture 8.1 Gravitation 1. Gravitational Force Lectue 8.1 Gavitation 1. Gavitational oce Duing ou discussion of foces we talked about gavitational foce acting on any object nea the eath's suface. We have aleady leaned that this foce povides the sae

More information

Net force on a charge due to several other charges: VECTOR SUM of all forces on that charge due to other charges Called Principle of SUPERPOSITON

Net force on a charge due to several other charges: VECTOR SUM of all forces on that charge due to other charges Called Principle of SUPERPOSITON REVIEW: ELECTRIC FORCE, ELECTRIC FIELD, ELECTRIC FIELD LINES, ELECTRIC FLUX, GAUSS S LAW, ELECTRIC POTENTIAL, CONTINUOUS CHARGE DISTRIBUTIONS (ELECTRIC FIELD, ELECTRIC POTENTIAL, GAUSS S LAW), ELECTRIC

More information

Hour Exam No.1. p 1 v. p = e 0 + v^b. Note that the probe is moving in the direction of the unit vector ^b so the velocity vector is just ~v = v^b and

Hour Exam No.1. p 1 v. p = e 0 + v^b. Note that the probe is moving in the direction of the unit vector ^b so the velocity vector is just ~v = v^b and Hou Exam No. Please attempt all of the following poblems befoe the due date. All poblems count the same even though some ae moe complex than othes. Assume that c units ae used thoughout. Poblem A photon

More information

Ch. 14: Gravitation (Beta Version 7/01) 14 Gravitation

Ch. 14: Gravitation (Beta Version 7/01) 14 Gravitation Ch. 14: Gavitation (Beta Vesion 7/01) 14 Gavitation The Milky Way galaxy is a disk-shaped collection of dust, planets, and billions of stas, including ou Sun and sola system. The foce that binds it o any

More information

(a) The centripetal acceleration of a point on the equator of the Earth is given by v2. The velocity of the earth can be found by taking the ratio of

(a) The centripetal acceleration of a point on the equator of the Earth is given by v2. The velocity of the earth can be found by taking the ratio of Homewok VI Ch. 7 - Poblems 15, 19, 22, 25, 35, 43, 51. Poblem 15 (a) The centipetal acceleation of a point on the equato of the Eath is given by v2. The velocity of the eath can be found by taking the

More information

In this section we shall look at the motion of a projectile MOTION IN FIELDS 9.1 PROJECTILE MOTION PROJECTILE MOTION

In this section we shall look at the motion of a projectile MOTION IN FIELDS 9.1 PROJECTILE MOTION PROJECTILE MOTION MOTION IN FIELDS MOTION IN FIELDS 9 9. Pojectile motion 9. Gavitational field, potential and enegy 9.3 Electic field, potential and enegy 9. PROJECTILE MOTION 9.. State the independence of the vetical

More information

Magnetic Field and Magnetic Forces. Young and Freedman Chapter 27

Magnetic Field and Magnetic Forces. Young and Freedman Chapter 27 Magnetic Field and Magnetic Foces Young and Feedman Chapte 27 Intoduction Reiew - electic fields 1) A chage (o collection of chages) poduces an electic field in the space aound it. 2) The electic field

More information

Part 1. Electric Charges, Forces and Fields. Forces of nature or A short journey back to Physics 111. Chapter 17. Forces of Nature.

Part 1. Electric Charges, Forces and Fields. Forces of nature or A short journey back to Physics 111. Chapter 17. Forces of Nature. Foces of Natue Electic Chages, Foces and Fields Chapte 17 Electic Chage Coulomb s Law Electic Field Electic Field Lines Flux of an Electic Field Physics 111: Analysis of motion - 3 key ideas Pat 1 Foces

More information

Conservation of Momentum II

Conservation of Momentum II Pupose: To veify the pinciples of Consevation of Momentum and Consevation of Enegy in Elastic and Inelastic Collisions, and to exploe Collisions in the Cente of Mass fame. Equipment: Cuved Tack Metal Ball

More information

The Quantum Mechanical Nature of the Law of Universal Gravitation and the Law of Coulomb s Interactions

The Quantum Mechanical Nature of the Law of Universal Gravitation and the Law of Coulomb s Interactions The Quantum echanical Natue of the Law of Univesal Gavitation and the Law of Coulomb s Inteactions Fayang Qiu Laboatoy of olecula Engineeing, and Laboatoy of Natual Poduct Synthesis, Guangzhou Institute

More information

AP Physics Test Magnetic Fields; Sources of Magnetic Field

AP Physics Test Magnetic Fields; Sources of Magnetic Field AP Physics Test Magnetic Fields; Souces of Magnetic Field Pat I. Multiple hoice (4 points each) hoose the one best answe to each of the following poblems. axis 2 A = 0.05 T 0.3 m 0.3 m 1 (AP). A squae

More information

Chapter 16 Gyroscopes and Angular Momentum

Chapter 16 Gyroscopes and Angular Momentum Chapte 16 Gyoscopes and Angula Momentum 16.1 Gyoscopes o fa, most of the examples and applications we have consideed concened the otation of igid bodies about a fixed axis, o a moving axis the diection

More information

Magnetic Forces. Physics 231 Lecture 7-1

Magnetic Forces. Physics 231 Lecture 7-1 Magnetic Foces Physics 231 Lectue 7-1 Magnetic Foces Chaged paticles expeience an electic foce when in an electic field egadless of whethe they ae moving o not moving Thee is anothe foce that chaged paticles

More information

KICKSTART PHYSICS SPACE 1. SPEED AND ESCAPE VELOCITY 2. PROJECTILE MOTION 3. ACCELERATION AND G-FORCES 4. C AND RELATIVITY 5.

KICKSTART PHYSICS SPACE 1. SPEED AND ESCAPE VELOCITY 2. PROJECTILE MOTION 3. ACCELERATION AND G-FORCES 4. C AND RELATIVITY 5. KICKSTART PHYSICS SPACE 1. SPEED AND ESCAPE VELOCITY 2. PROJECTILE MOTION 3. ACCELERATION AND G-FORCES 4. C AND RELATIVITY 5. EINSTEIN Kickstat would like to acknowledge and pay espect to the taditional

More information

General Physics (PHY 2130)

General Physics (PHY 2130) Geneal Physics (PHY 130) Lectue 11 Rotational kinematics and unifom cicula motion Angula displacement Angula speed and acceleation http://www.physics.wayne.edu/~apetov/phy130/ Lightning Review Last lectue:

More information

Orbital Motion & Gravity

Orbital Motion & Gravity Astonomy: Planetay Motion 1 Obital Motion D. Bill Pezzaglia A. Galileo & Fee Fall Obital Motion & Gavity B. Obits C. Newton s Laws Updated: 013Ma05 D. Einstein A. Galileo & Fee Fall 3 1. Pojectile Motion

More information

The Schwarzschild Metric

The Schwarzschild Metric The Schwazschild Metic Relativity and Astophysics Lectue 34 Tey Hete Outline Schwazschild metic Spatial pat Time pat Coodinate Fames Fee-float Shell Schwazschild bookkeepe Pinciple of Extemal Aging Consevation

More information

Physics Mechanics

Physics Mechanics Physics 111 -- Mechanics Lectue: Tom Humanic Contact info: Office: Physics Reseach Building, Rm. 2144 Email: humanic@mps.ohio-state.edu Phone: 614 247 8950 Office hous: Tuesday 4:30 pm My lectue slides

More information

Conservation of Momentum

Conservation of Momentum Physics 7 Consevation of Momentum Intoduction Collisions occu all aound us and on many size scales. We obseve them in ou eveyday wold as ca accidents, battes hitting a baseball out of the ballpak, aindops

More information