TRAVELING WAVES. Chapter Simple Wave Motion. Waves in which the disturbance is parallel to the direction of propagation are called the

Size: px
Start display at page:

Download "TRAVELING WAVES. Chapter Simple Wave Motion. Waves in which the disturbance is parallel to the direction of propagation are called the"

Transcription

1 Chapte 15 RAVELING WAVES 15.1 Simple Wave Motion Wave in which the ditubance i pependicula to the diection of popagation ae called the tanvee wave. Wave in which the ditubance i paallel to the diection of popagation ae called the longitudinal wave. 1

2 Wave pule t =, y = f(x) t >, y = f(x-vt) Fo wave pule on a ope, the peed of wave v = F / µ, whee F i the tenion, µ i the linea ma denity (ma pe unit length). Example 1. When will the pule each the left pole if the ma of the ope i.5 kg and the ma of the hanging weight i 1 kg?

3 he pule tavel with the peed v = F / µ. he tenion i F = mg = N = 98.1 N. he linea denity of ma i µ = m ope / L ope =.5/ 5 kg / m =. kg / m hen the peed of pule i v = F / µ = 98.1/. m / = 7.4 m / and the popagation time i t = m / 7.4 m / =.9. 3

4 Fo ound wave in liquid and gae, v = B / ρ whee B i the bulk modulu and ρ i the denity. In ideal gae the bulk modulu i popotional to the peue and (Chapte 17) v = γ R / M whee i the abolute tempeatue in K, M i the mola ma (ma of 1 mol γ of the ga), R = J/(mol K) i the univeal ga contant and = 1.4 fo diatomic gae ( γ = 1.67 fo monatomic gae). = Example. Calculate peed of ound in ai at o C. Fo ai, the mola ma M = 9x1-3 kg/mol, = (73 + ) K = 93 K, and 3 ( ) v = γ R / M = / 9 1 m / = 343 m / (at o C, v = 331 m/). 4

5 he Wave Equation y = v y t x Any function y = y ( x vt ) y ( α ) atifie thi equation. Indeed, Similaly, = = v y dy α dy t d α t d α ( ) ( ), = v = v = v y dy d dy α d y t t d α d α d α t d α = = y dy α dy x d α x d α Combining, we get the wave equation ( ) ( ), = = = y dy d dy α d y x x d α d α d α x d α y = v y t x 5

6 15. Peiodic Wave Hamonic (inuoidal) wave he minimum ditance afte which the wave epeat i called the wavelength λ Duing the peiod = 1/f the wave move a ditance of one wavelength: λ v = = f λ = ωλ / π he hamonic (inuoidal) taveling wave ha the hape whee ( ) = ( π x ω ) ( ω ) ( ) y x t A t A kx t A k x vt, in in in ( ) k = π / λ = ω / v = π f / v i called the wave numbe. λ y he velocity of a point in the wave i v x = t = ω A co ( kx ω t ) y and the acceleation of thi point i a = = ω A in ( kx ω t ) x t 6

7 Example 3. he wave function fo a hamonic wave on a ting i Find paamete of the wave. 1 1 (, ) = (.1 ) in ( 4.1 ) ( 9. ) y x t m m x t he amplitude A =.1m. he wave numbe k = 4.1 m -1 and the wavelength λ = π / k = 1.53 m. ω = = π / ω =.74. he fequency and hen the peed of the wave λ ω 9. v = k = 4.1 m / =.4 m / 7

8 Enegy anfe via Wave he ate of enegy tanfe i powe, P = u F v t he vecto component ae u $ x y $, $, F = F i + F j v = v j t t P = F v in y t = F θ v t At mall angle, in θ tan θ = In the end, the powe u P = F v = F tan θ v = F y x y y t t x t ( ω ) ω ( ω ) = F ka co kx t A co kx t he tenion can be expeed via the wave peed v uing v = F / µ. hen and the aveage powe i co ( ) P = µ v ω A kx ω t P = µ v ω A av 1 8

9 he enegy tavel along the ting at the wave peed v he aveage enegy E t flowing pat a point in time x E = P t = µ v ω A t ( ) 1 av av x v t = hi enegy i ditibuted ove the length o the aveage enegy in the length i ( ) µω E = A x av 1 Example 4. A wave of wavelength 4 cm and amplitude.8 cm move along a 1 m egment of a 75 m ting with ma 3 g and tenion 1 N. What ae the paamete of the wave including the aveage total enegy? he peed of the wave i given by tenion and ma denity: ( ) v = F / µ = 1/.3/ 75 m / = m / he angula fequency i ω = π v / λ = /.4 ad / = ad / hen the aveage total enegy i.3 ( E ) = 1 1 µω A x = 75 ( ) (.8 ) 1 J =.86 J av 9

10 Hamonic Sound Wave he diplacement of molecule fom thei equilibium poition, ( ) ( ) x, t = in kx ω t, i out of phae by 9 o degee with the peue and denity wave, ( ) ( ) p x, t = p in kx ω t π /, whee p i the change in peue fom the equilibium. he amplitude p = ρω v he enegy and the enegy denity of ound wave ae E = ρω V u = ρω, av ( ) 1 1 av 1

11 15.3 Wave in hee Dimenion he motion of wavefont can be epeented by the ay pependicula to the wavefont. he aveage powe in the wave pe unit aea that i pependicula to the diection of popagation, i called the intenity, I P av / A W / m = If a point ouce emit unifomly in all diection, then the wavefont ae pheical, A = 4 π, and the intenity at a ditance fom the ouce i I = P / 4 π av 11

12 hee i a link between intenity and enegy denity: In the hell, whee we ued E = u V = u Av t av av av P = E / t = u Av, av av av I = P / A = u v = p / ρ v av av av 1, u = ρω = p ρω v 1, / 1

13 Example 5. A peake diaphagm 5 cm in diamete i vibating at 1 khz with an amplitude.15 mm. Find the paamete of the ound wave immediately in font of the peake and intenity at a ditance 5 m. he peue amplitude i ( )( )( )( ) p = ρω v = 1.9 kg / m π 1 34 m / m = N / m he intenity at the diaphagm i ρ ( ) ( ) 1 1 I = p / v = / W / m = W / m he powe of the peake i the intenity multiplied by the aea of the diaphagm, ( ) P = IA = π.5 / 4 W =.38 W hen the intenity at a ditance 5 m, auming the unifom adiation in the fowad hemiphee, i ( ) ( ) I 5 m = P / π =.38 / W / m =.43 mw / m 13

14 he intenity level of ound i meaued in decibel defined a β = 1log I I whee the efeence level I i uually taken a thehold of heaing, I = 1 W / m 1 Example 6. Find the intenity level of ound at a ditance 5 m fom the peake fom Example 5. he intenity I W m 3 =. hen the intenity level 5 m.43 1 / β ( 9 ) ( 3 1 ) I = 1 log = 1 log.43 1 /1 db I 1 log.43 1 db = db = 93.8 db 14

15 15.4 Wave Encounteing Baie When a wave encounte an obtacle, pat of it i eflected and pat i tanmitted though: Hee the eflected pule i inveted; the tanmitted pule i not (the econd ting i heavie) Hee both the eflected and tanmitted pule ae not inveted (the econd ting i lighte) 15

16 Example 7. he incident wave with amplitude A encounte the junction of two wie with the ame tenion F. he wave peed in the fit wie i thee time that in the econd, and the amplitude of the eflected wave i a quate of the amplitude of the incident wave. What i the amplitude of the tanmitted wave? By enegy conevation, the incident powe i equal to the um of powe in eflected and tanmitted wave, 3 P P P P µ v ω A 1 i = + t, av =, µ 1 v 1 ω A i = µ 1 v 1 ω A + µ v ω A t Since the wave peed v = F / µ, and the tenion i the ame in both wie, v A = v A + v A = + A A F F F A i t v i v v t v v v We know that A = A i / 4, v 1 = 3 v. heefoe, 1 1 ( ) i i t i A A / 4 A 1 A 5 v = v + v /3 = v A t A t = 16 A i

17 Diffaction Bending of a wavefont behind an obtacle i called diffaction. Almot all of the diffaction occu within eveal wavelength fom the edge of the obtacle Flat wavefont paing though a mall apetue bend, pead out, and become pheical. he lage i the wavelength in compaion to the apetue, the lage ae the diffaction effect. 17

18 he appoximation that wave popagate in taight line without diffaction i called the ay appoximation (zeo wavelength appoximation). Fo ound wave, λ 3 cm 3 m and fo viible light λ m 18

19 15. 5 he Dopple Effect Change in fequency of the eceived ignal in compaion to the fequency of the emitted ignal, which eult fom a elative motion of the ouce and eceive, i called the Dopple effect. If the ouce and eceive move cloe togethe, the eceived fequency i geate than the ouce fequency. If the ouce and eceive move away fom each othe, the eceived fequency i lowe than the ouce fequency. 19

20 Example 1. Souce move to the ight with u ; eceive i tationay; peed of the wave i v; the time between emiion of two conecutive cet i. Between two conecutive event, the fit cet move v while the ouce move u. hu, the ditance between two cet (the wavelength) i hen the fequency in the eceive λ = ( v ± u ) ( ) = v ± u / f f = v / = f λ ± v v u (+ the eceive behind the ouce, - in font) Example. Souce doe not move; eceive move with u ; peed of the wave i v; the time between aival of two conecutive cet i. Between detecting two conecutive cet, the eceive move by u while the fit cet move by v. he ditance between two cet i the wavelength λ = v ± u (- eceive move away fom the ouce, + it move towad the ouce). hu the fequency i f 1 / ( ) / ( ) = = v ± u λ = f v ± u / v

21 Example 3. If both move, v u ± ± f = f v u he pope ign ae choen by emembeing that the fequency goe up when the ouce move towad the eceive and the eceive towad the ouce. If both u, u v ± f v f u Example 4. he fequency of ca hon i 5 Hz. Find the fequency and the wavelength of the eceived ignal if the ca move towad eceive with u = 9 km/h. he ca velocity i 9 km/h =9 (1 m)/(36 ) = 5 m/ he wavelength in font of the ca ( ) ( ) λ = v u / f = 34 5 / 5 m =.63 m and the eceived fequency i λ f = v / = f = 5 Hz = 54 Hz v v u

22 Example 5. he ame if the honking ca i tationay while the eceive move towad thi ca with u = 6 km/h 6 km/h = 6(1)/36 m/ =16.7 m/ he eceived fequency i ( ) ( ) f = f v ± u / v = / 34 Hz = 55 Hz Example 6. he ca peed away fom the police ca. he ada unit emit the electomagnetic wave with fequency f. Find the peed of the ca u if the fequency of eflected wave, eceived by the ada unit, i f f. he ada wave tike the peeding ca at a fequency f = f v ± u v = f c u c = f ( ) / ( ) / ( 1 u ) c and ae eflected fom (emitted by) the ca with the ame fequency. he eceived ignal by the police i then ( ) ( ) ( ) ( ) f ' = f = f = f 1 f = 1 f 1 1 f v c 1 u u u u v ± u c + u 1 + u / c c c c c heefoe, f = f ' u f = c f and u = c f f

23 Dopple Shift and Relativity In non-elativitic ytem, the Dopple effect i detemined by the peed of both the ouce and the eceive elative to the medium which affected the peed of popagation of wave. Fo light and othe electomagnetic wave the peed of popagation c i a univeal contant which doe not depend on the peed of ouce o eceive (no wind ). Second, the time between the event uch a emiion of wave cet,, depend on the efeence fame and i diffeent in the efeence fame of ouce and eceive. In the end, the Dopple hift fo electomagnetic wave depend only on the elative velocity of the ouce and eceive u: f f c ± u = c m u whee ign i uch o that the fequency goe up when the ouce and eceive ae appoaching each othe. 3

24 Chapte 15 eview Wave on a ting: v = F / µ Sound wave in liquid and gae: v = B / ρ Sound wave in dilute ideal gae: v = γ R / M Electomagnetic wave: the peed i a univeal contant, c = 3x1 8 m/ Wave equation: = v y y t x Paamete of hamonic wave ( ) ( ) y x, t = A in kx ±ω t : k = π / λ = ω / v, ω = π f = π / = kv, v = f λ = ω / k = πωλ = λ / he enegy in hamonic wave i popotional to the quae of the amplitude P = 1/ µ v ω A Powe fo wave on the ting: ( ) av Enegy denity fo ound wave: ( ) av 1/ ρω, ρω u = p = v 4

25 I = P / A Intenity fo ound wave: av Sound intenity level: β ( ) I = u av v = 1log I / I, I = 1 W / m 1 Dopple effect v ± u f = v ± u f Moving ouce: λ = ( v ± u ) / f f = v ± u / λ = f v ± u / v Moving eceive: ( ) ( ) Small peed of ouce o eceive: f / f ± u / v 5

Phys101 Lectures 30, 31. Wave Motion

Phys101 Lectures 30, 31. Wave Motion Phys0 Lectues 30, 3 Wave Motion Key points: Types of Waves: Tansvese and Longitudinal Mathematical Repesentation of a Taveling Wave The Pinciple of Supeposition Standing Waves; Resonance Ref: -7,8,9,0,,6,,3,6.

More information

Lecture No. 6 (Waves) The Doppler Effect

Lecture No. 6 (Waves) The Doppler Effect Lectue No. 6 (Wave) The Dopple Eect 1) A ound ouce i moving at 80 m/ towad a tationay litene that i tanding in till ai. (a) Find the wavelength o the ound in the egion between the ouce and the litene.

More information

Chapter 19 Webassign Help Problems

Chapter 19 Webassign Help Problems Chapte 9 Webaign Help Poblem 4 5 6 7 8 9 0 Poblem 4: The pictue fo thi poblem i a bit mileading. They eally jut give you the pictue fo Pat b. So let fix that. Hee i the pictue fo Pat (a): Pat (a) imply

More information

Class XII - Physics Wave Optics Chapter-wise Problems. Chapter 10

Class XII - Physics Wave Optics Chapter-wise Problems. Chapter 10 Class XII - Physics Wave Optics Chapte-wise Poblems Answes Chapte (c) (a) 3 (a) 4 (c) 5 (d) 6 (a), (b), (d) 7 (b), (d) 8 (a), (b) 9 (a), (b) Yes Spheical Spheical with huge adius as compaed to the eath

More information

Honors Classical Physics I

Honors Classical Physics I Hono Claical Phyic I PHY141 Lectue 9 Newton Law of Gavity Pleae et you Clicke Channel to 1 9/15/014 Lectue 9 1 Newton Law of Gavity Gavitational attaction i the foce that act between object that have a

More information

Simulation of Spatially Correlated Large-Scale Parameters and Obtaining Model Parameters from Measurements

Simulation of Spatially Correlated Large-Scale Parameters and Obtaining Model Parameters from Measurements Simulation of Spatially Coelated Lage-Scale Paamete and Obtaining Model Paamete fom PER ZETTERBERG Stockholm Septembe 8 TRITA EE 8:49 Simulation of Spatially Coelated Lage-Scale Paamete and Obtaining Model

More information

Circular Motion. Mr. Velazquez AP/Honors Physics

Circular Motion. Mr. Velazquez AP/Honors Physics Cicula Motion M. Velazquez AP/Honos Physics Objects in Cicula Motion Accoding to Newton s Laws, if no foce acts on an object, it will move with constant speed in a constant diection. Theefoe, if an object

More information

LECTURE 14. m 1 m 2 b) Based on the second law of Newton Figure 1 similarly F21 m2 c) Based on the third law of Newton F 12

LECTURE 14. m 1 m 2 b) Based on the second law of Newton Figure 1 similarly F21 m2 c) Based on the third law of Newton F 12 CTU 4 ] NWTON W O GVITY -The gavity law i foulated fo two point paticle with ae and at a ditance between the. Hee ae the fou tep that bing to univeal law of gavitation dicoveed by NWTON. a Baed on expeiental

More information

A) At each point along the pipe, the volume of fluid passing by is given by dv dt = Av, thus, the two velocities are: v n. + ρgy 1

A) At each point along the pipe, the volume of fluid passing by is given by dv dt = Av, thus, the two velocities are: v n. + ρgy 1 1) The horizontal pipe hon in Fig. 1 ha a diameter of 4.8 cm at the ider portion and 3.7 cm at the contriction. Water i floing in the pipe and the dicharge from the pipe i 6.50 x -3 m 3 /. A) Find the

More information

Solutions Practice Test PHYS 211 Exam 2

Solutions Practice Test PHYS 211 Exam 2 Solution Pactice Tet PHYS 11 Exam 1A We can plit thi poblem up into two pat, each one dealing with a epaate axi. Fo both the x- and y- axe, we have two foce (one given, one unknown) and we get the following

More information

11) A thin, uniform rod of mass M is supported by two vertical strings, as shown below.

11) A thin, uniform rod of mass M is supported by two vertical strings, as shown below. Fall 2007 Qualifie Pat II 12 minute questions 11) A thin, unifom od of mass M is suppoted by two vetical stings, as shown below. Find the tension in the emaining sting immediately afte one of the stings

More information

Test 2 phy a) How is the velocity of a particle defined? b) What is an inertial reference frame? c) Describe friction.

Test 2 phy a) How is the velocity of a particle defined? b) What is an inertial reference frame? c) Describe friction. Tet phy 40 1. a) How i the velocity of a paticle defined? b) What i an inetial efeence fae? c) Decibe fiction. phyic dealt otly with falling bodie. d) Copae the acceleation of a paticle in efeence fae

More information

Uniform Circular Motion

Uniform Circular Motion Unifom Cicula Motion Intoduction Ealie we defined acceleation as being the change in velocity with time: a = v t Until now we have only talked about changes in the magnitude of the acceleation: the speeding

More information

Boise State University Department of Electrical and Computer Engineering ECE470 Electric Machines

Boise State University Department of Electrical and Computer Engineering ECE470 Electric Machines Boie State Univeity Depatment of Electical and Compute Engineeing ECE470 Electic Machine Deivation of the Pe-Phae Steady-State Equivalent Cicuit of a hee-phae Induction Machine Nomenclatue θ: oto haft

More information

Laser Doppler Velocimetry (LDV)

Laser Doppler Velocimetry (LDV) AeE 545 cla note #1 Lae Dopple elocimety (LD) Pat - 01 Hui Hu Depatment o Aeopace Engineeing, Iowa State Univeity Ame, Iowa 50011, U.S.A Technique o Flow elocity Meauement Intuive technique Pitot-tatic

More information

AE 423 Space Technology I Chapter 2 Satellite Dynamics

AE 423 Space Technology I Chapter 2 Satellite Dynamics AE 43 Space Technology I Chapte Satellite Dynamic.1 Intoduction In thi chapte we eview ome dynamic elevant to atellite dynamic and we etablih ome of the baic popetie of atellite dynamic.. Dynamic of a

More information

Rotational Motion. Lecture 6. Chapter 4. Physics I. Course website:

Rotational Motion. Lecture 6. Chapter 4. Physics I. Course website: Lectue 6 Chapte 4 Physics I Rotational Motion Couse website: http://faculty.uml.edu/andiy_danylov/teaching/physicsi Today we ae going to discuss: Chapte 4: Unifom Cicula Motion: Section 4.4 Nonunifom Cicula

More information

Physics 207 Lecture 5. Lecture 5

Physics 207 Lecture 5. Lecture 5 Lectue 5 Goals: Addess sstems with multiple acceleations in 2- dimensions (including linea, pojectile and cicula motion) Discen diffeent efeence fames and undestand how the elate to paticle motion in stationa

More information

Lecture Principles of scattering and main concepts.

Lecture Principles of scattering and main concepts. Lectue 15. Light catteing and aboption by atmopheic paticuate. Pat 1: Pincipe of catteing. Main concept: eementay wave, poaization, Stoke matix, and catteing phae function. Rayeigh catteing. Objective:

More information

Physics 121 Hour Exam #5 Solution

Physics 121 Hour Exam #5 Solution Physics 2 Hou xam # Solution This exam consists of a five poblems on five pages. Point values ae given with each poblem. They add up to 99 points; you will get fee point to make a total of. In any given

More information

( ) rad ( 2.0 s) = 168 rad

( ) rad ( 2.0 s) = 168 rad .) α 0.450 ω o 0 and ω 8.00 ω αt + ω o o t ω ω o α HO 9 Solution 8.00 0 0.450 7.8 b.) ω ω o + αδθ o Δθ ω 8.00 0 ω o α 0.450 7. o Δθ 7. ev.3 ev π.) ω o.50, α 0.300, Δθ 3.50 ev π 7π ev ω ω o + αδθ o ω ω

More information

A moving charged particle creates a magnetic field vector at every point in space except at its position.

A moving charged particle creates a magnetic field vector at every point in space except at its position. 1 Pat 3: Magnetic Foce 3.1: Magnetic Foce & Field A. Chaged Paticles A moving chaged paticle ceates a magnetic field vecto at evey point in space ecept at its position. Symbol fo Magnetic Field mks units

More information

A new force Magnetic force. Today. Force Fields: A disturbance of space. The correspondence of a loop of current and magnet.

A new force Magnetic force. Today. Force Fields: A disturbance of space. The correspondence of a loop of current and magnet. Today A new foce Magnetic foce Announcements HW#6 and HW#7 ae both due Wednesday Mach 18th. Thanks to my being WAY behind schedule, you 2nd exam will be a take-home exam! Stay tuned fo details Even if

More information

Section 25 Describing Rotational Motion

Section 25 Describing Rotational Motion Section 25 Decibing Rotational Motion What do object do and wh do the do it? We have a ve thoough eplanation in tem of kinematic, foce, eneg and momentum. Thi include Newton thee law of motion and two

More information

Static Electric Fields. Coulomb s Law Ε = 4πε. Gauss s Law. Electric Potential. Electrical Properties of Materials. Dielectrics. Capacitance E.

Static Electric Fields. Coulomb s Law Ε = 4πε. Gauss s Law. Electric Potential. Electrical Properties of Materials. Dielectrics. Capacitance E. Coulomb Law Ε Gau Law Electic Potential E Electical Popetie of Mateial Conducto J σe ielectic Capacitance Rˆ V q 4πε R ρ v 2 Static Electic Field εe E.1 Intoduction Example: Electic field due to a chage

More information

Waves and Polarization in General

Waves and Polarization in General Waves and Polaization in Geneal Wave means a distubance in a medium that tavels. Fo light, the medium is the electomagnetic field, which can exist in vacuum. The tavel pat defines a diection. The distubance

More information

e.g: If A = i 2 j + k then find A. A = Ax 2 + Ay 2 + Az 2 = ( 2) = 6

e.g: If A = i 2 j + k then find A. A = Ax 2 + Ay 2 + Az 2 = ( 2) = 6 MOTION IN A PLANE 1. Scala Quantities Physical quantities that have only magnitude and no diection ae called scala quantities o scalas. e.g. Mass, time, speed etc. 2. Vecto Quantities Physical quantities

More information

Homework 7 Solutions

Homework 7 Solutions Homewok 7 olutions Phys 4 Octobe 3, 208. Let s talk about a space monkey. As the space monkey is oiginally obiting in a cicula obit and is massive, its tajectoy satisfies m mon 2 G m mon + L 2 2m mon 2

More information

FI 2201 Electromagnetism

FI 2201 Electromagnetism FI Electomagnetim Aleande A. Ikanda, Ph.D. Phyic of Magnetim and Photonic Reeach Goup ecto Analyi CURILINEAR COORDINAES, DIRAC DELA FUNCION AND HEORY OF ECOR FIELDS Cuvilinea Coodinate Sytem Cateian coodinate:

More information

ASTR 3740 Relativity & Cosmology Spring Answers to Problem Set 4.

ASTR 3740 Relativity & Cosmology Spring Answers to Problem Set 4. ASTR 3740 Relativity & Comology Sping 019. Anwe to Poblem Set 4. 1. Tajectoie of paticle in the Schwazchild geomety The equation of motion fo a maive paticle feely falling in the Schwazchild geomety ae

More information

Ch 30 - Sources of Magnetic Field! The Biot-Savart Law! = k m. r 2. Example 1! Example 2!

Ch 30 - Sources of Magnetic Field! The Biot-Savart Law! = k m. r 2. Example 1! Example 2! Ch 30 - Souces of Magnetic Field 1.) Example 1 Detemine the magnitude and diection of the magnetic field at the point O in the diagam. (Cuent flows fom top to bottom, adius of cuvatue.) Fo staight segments,

More information

Simple Harmonic Mo/on. Mandlebrot Set (image courtesy of Wikipedia)

Simple Harmonic Mo/on. Mandlebrot Set (image courtesy of Wikipedia) Simple Hamonic Mo/on Mandlebot Set (image coutesy of Wikipedia) Oscilla/ons Oscilla/on the mo/on of an object that egulaly epeats itself, back and foth, ove the same path. We say that mo/on is peiodic,

More information

Advanced Subsidiary GCE (H157) Advanced GCE (H557) Physics B (Advancing Physics) Data, Formulae and Relationships Booklet

Advanced Subsidiary GCE (H157) Advanced GCE (H557) Physics B (Advancing Physics) Data, Formulae and Relationships Booklet Advanced Subsidiay GCE (H57) Advanced GCE (H557) Physics B (Advancing Physics) Data, Fomulae and Relationships Booklet The infomation in this booklet is fo the use of candidates following the Advanced

More information

EP225 Note No. 5 Mechanical Waves

EP225 Note No. 5 Mechanical Waves EP5 Note No. 5 Mechanical Wave 5. Introduction Cacade connection of many ma-pring unit conitute a medium for mechanical wave which require that medium tore both kinetic energy aociated with inertia (ma)

More information

Black Body Radiation and Radiometric Parameters:

Black Body Radiation and Radiometric Parameters: Black Body Radiation and Radiometic Paametes: All mateials absob and emit adiation to some extent. A blackbody is an idealization of how mateials emit and absob adiation. It can be used as a efeence fo

More information

Announcements. Description Linear Angular position x θ displacement x θ rate of change of position v x ω x = = θ average rate of change of position

Announcements. Description Linear Angular position x θ displacement x θ rate of change of position v x ω x = = θ average rate of change of position Announcement In the lectue link Look o tet 1 beakdown liting the topic o the quetion. Look o m umma o topic o the eam. We ll ue it on the eiew net Tueda. Look o a lit o baic phic act eleant o thi eam.

More information

Objective Notes Summary

Objective Notes Summary Objective Notes Summay An object moving in unifom cicula motion has constant speed but not constant velocity because the diection is changing. The velocity vecto in tangent to the cicle, the acceleation

More information

b) (5) What average force magnitude was applied by the students working together?

b) (5) What average force magnitude was applied by the students working together? Geneal Physics I Exam 3 - Chs. 7,8,9 - Momentum, Rotation, Equilibium Nov. 3, 2010 Name Rec. Inst. Rec. Time Fo full cedit, make you wok clea to the gade. Show fomulas used, essential steps, and esults

More information

OSCILLATIONS AND GRAVITATION

OSCILLATIONS AND GRAVITATION 1. SIMPLE HARMONIC MOTION Simple hamonic motion is any motion that is equivalent to a single component of unifom cicula motion. In this situation the velocity is always geatest in the middle of the motion,

More information

Formula Formula symbols Units. s = F A. e = x L. E = s ε. k = F δ. G = t γ. e = at. maximum load original cross sectional area. s M E = = N/m.

Formula Formula symbols Units. s = F A. e = x L. E = s ε. k = F δ. G = t γ. e = at. maximum load original cross sectional area. s M E = = N/m. A Lit of foulae fo ecanical engineeing pinciple Foula Foula ybol Unit Ste Stain applied foce co ectionalaea cange in lengt oiginal lengt F A e x L Young odulu of elaticity te tain Stiffne foce extenion

More information

Galilean Transformation vs E&M y. Historical Perspective. Chapter 2 Lecture 2 PHYS Special Relativity. Sep. 1, y K K O.

Galilean Transformation vs E&M y. Historical Perspective. Chapter 2 Lecture 2 PHYS Special Relativity. Sep. 1, y K K O. PHYS-2402 Chapte 2 Lectue 2 Special Relativity 1. Basic Ideas Sep. 1, 2016 Galilean Tansfomation vs E&M y K O z z y K In 1873, Maxwell fomulated Equations of Electomagnetism. v Maxwell s equations descibe

More information

SPH3UW/SPH4U Unit 3.2 Forces in Cetripetal Motion Page 1 of 6. Notes Physics Tool Box

SPH3UW/SPH4U Unit 3.2 Forces in Cetripetal Motion Page 1 of 6. Notes Physics Tool Box SPH3UW/SPH4U Unit 3. Foce in Cetipetal Motion Page 1 o 6 Note Phyic Tool Box Net Foce: acting on an object in uniom cicula motion act towad the cente o the cicle. Magnitude o Net Foce: combine Newton Second

More information

F g. = G mm. m 1. = 7.0 kg m 2. = 5.5 kg r = 0.60 m G = N m 2 kg 2 = = N

F g. = G mm. m 1. = 7.0 kg m 2. = 5.5 kg r = 0.60 m G = N m 2 kg 2 = = N Chapte answes Heinemann Physics 4e Section. Woked example: Ty youself.. GRAVITATIONAL ATTRACTION BETWEEN SMALL OBJECTS Two bowling balls ae sitting next to each othe on a shelf so that the centes of the

More information

15 B1 1. Figure 1. At what speed would the car have to travel for resonant oscillations to occur? Comment on your answer.

15 B1 1. Figure 1. At what speed would the car have to travel for resonant oscillations to occur? Comment on your answer. Kiangsu-Chekiang College (Shatin) F:EasteHolidaysAssignmentAns.doc Easte Holidays Assignment Answe Fom 6B Subject: Physics. (a) State the conditions fo a body to undego simple hamonic motion. ( mak) (a)

More information

3. Electromagnetic Waves II

3. Electromagnetic Waves II Lectue 3 - Electomagnetic Waves II 9 3. Electomagnetic Waves II Last time, we discussed the following. 1. The popagation of an EM wave though a macoscopic media: We discussed how the wave inteacts with

More information

Gravity. David Barwacz 7778 Thornapple Bayou SE, Grand Rapids, MI David Barwacz 12/03/2003

Gravity. David Barwacz 7778 Thornapple Bayou SE, Grand Rapids, MI David Barwacz 12/03/2003 avity David Bawacz 7778 Thonapple Bayou, and Rapid, MI 495 David Bawacz /3/3 http://membe.titon.net/daveb Uing the concept dicued in the peceding pape ( http://membe.titon.net/daveb ), I will now deive

More information

Uniform Circular Motion

Uniform Circular Motion Unifom Cicula Motion Have you eve idden on the amusement pak ide shown below? As it spins you feel as though you ae being pessed tightly against the wall. The ide then begins to tilt but you emain glued

More information

Graphs of Sine and Cosine Functions

Graphs of Sine and Cosine Functions Gaphs of Sine and Cosine Functions In pevious sections, we defined the tigonometic o cicula functions in tems of the movement of a point aound the cicumfeence of a unit cicle, o the angle fomed by the

More information

School of Electrical and Computer Engineering, Cornell University. ECE 303: Electromagnetic Fields and Waves. Fall 2007

School of Electrical and Computer Engineering, Cornell University. ECE 303: Electromagnetic Fields and Waves. Fall 2007 School of Electical and Compute Engineeing, Conell Univesity ECE 33: Electomagnetic Fields and Waves Fall 7 Homewok 6 Due on Oct. 5, 7 by 5: PM Reading Assignments: i) Review the lectue notes. ii) Review

More information

SAMPLE PAPER I. Time Allowed : 3 hours Maximum Marks : 70

SAMPLE PAPER I. Time Allowed : 3 hours Maximum Marks : 70 SAMPL PAPR I Time Allowed : 3 hous Maximum Maks : 70 Note : Attempt All questions. Maks allotted to each question ae indicated against it. 1. The magnetic field lines fom closed cuves. Why? 1 2. What is

More information

Ch 13 Universal Gravitation

Ch 13 Universal Gravitation Ch 13 Univesal Gavitation Ch 13 Univesal Gavitation Why do celestial objects move the way they do? Keple (1561-1630) Tycho Bahe s assistant, analyzed celestial motion mathematically Galileo (1564-1642)

More information

Circular Motion & Torque Test Review. The period is the amount of time it takes for an object to travel around a circular path once.

Circular Motion & Torque Test Review. The period is the amount of time it takes for an object to travel around a circular path once. Honos Physics Fall, 2016 Cicula Motion & Toque Test Review Name: M. Leonad Instuctions: Complete the following woksheet. SHOW ALL OF YOUR WORK ON A SEPARATE SHEET OF PAPER. 1. Detemine whethe each statement

More information

RE 7.a. RE 7.b Energy Dissipation & Resonance RE 7.c EP7, HW7: Ch 7 Pr s 31, 32, 45, 62 & CP

RE 7.a. RE 7.b Energy Dissipation & Resonance RE 7.c EP7, HW7: Ch 7 Pr s 31, 32, 45, 62 & CP Wed. Lab Fi. Mon. Tue. 7.-.4 Macocopic Enegy Quiz 6 4pm, hee Math & Phy Reeach L6 Wok and Enegy 7.5-.9 Enegy Tanfe RE 7.a RE 7.b 7.0-. Enegy Diipation & Reonance RE 7.c EP7, HW7: Ch 7 P 3, 3, 45, 6 & CP

More information

Section 11. Timescales Radiation transport in stars

Section 11. Timescales Radiation transport in stars Section 11 Timescales 11.1 Radiation tanspot in stas Deep inside stas the adiation eld is vey close to black body. Fo a black-body distibution the photon numbe density at tempeatue T is given by n = 2

More information

School of Electrical and Computer Engineering, Cornell University. ECE 303: Electromagnetic Fields and Waves. Fall 2007

School of Electrical and Computer Engineering, Cornell University. ECE 303: Electromagnetic Fields and Waves. Fall 2007 School of Electical and Compute Engineeing, Conell Univesity ECE 303: Electomagnetic Fields and Waves Fall 007 Homewok 8 Due on Oct. 19, 007 by 5:00 PM Reading Assignments: i) Review the lectue notes.

More information

( )( )( ) ( ) + ( ) ( ) ( )

( )( )( ) ( ) + ( ) ( ) ( ) 3.7. Moel: The magnetic fiel is that of a moving chage paticle. Please efe to Figue Ex3.7. Solve: Using the iot-savat law, 7 19 7 ( ) + ( ) qvsinθ 1 T m/a 1.6 1 C. 1 m/s sin135 1. 1 m 1. 1 m 15 = = = 1.13

More information

RIGID-ROTOR VLASOV EQUILIBRIUM FOR AN INTENSE CHARGED-PARTICLE BEAM PROPAGATING THROUGH A PERIODIC SOLENOIDAL MAGNETIC FIELD

RIGID-ROTOR VLASOV EQUILIBRIUM FOR AN INTENSE CHARGED-PARTICLE BEAM PROPAGATING THROUGH A PERIODIC SOLENOIDAL MAGNETIC FIELD RIGID-ROTOR VLASOV EQUILIBRIUM FOR AN INTENSE CHARGED-PARTICLE BEAM PROPAGATING THROUGH A PERIODIC SOLENOIDAL MAGNETIC FIELD Chiping Chen and Renato Pakte Plama Science and Fuion Cente Maachuett Intitute

More information

How can you find the dimensions of a square or a circle when you are given its area? When you multiply a number by itself, you square the number.

How can you find the dimensions of a square or a circle when you are given its area? When you multiply a number by itself, you square the number. 7. Finding Squae Root How can you find the dimenion of a quae o a cicle when you ae given it aea? When you multiply a numbe by itelf, you quae the numbe. Symbol fo quaing i the exponent. = = 6 quaed i

More information

Midterm Exam #2, Part A

Midterm Exam #2, Part A Physics 151 Mach 17, 2006 Midtem Exam #2, Pat A Roste No.: Scoe: Exam time limit: 50 minutes. You may use calculatos and both sides of ONE sheet of notes, handwitten only. Closed book; no collaboation.

More information

1 2 U CV. K dq I dt J nqv d J V IR P VI

1 2 U CV. K dq I dt J nqv d J V IR P VI o 5 o T C T F 9 T K T o C 7.5 L L T V VT Q mct nct Q F V ml F V dq A H k TH TC dt L pv nt Kt nt CV ideal monatomic gas 5 CV ideal diatomic gas w/o vibation V W pdv V U Q W W Q e Q Q e Canot H C T T S C

More information

1 Fundamental Solutions to the Wave Equation

1 Fundamental Solutions to the Wave Equation 1 Fundamental Solutions to the Wave Equation Physical insight in the sound geneation mechanism can be gained by consideing simple analytical solutions to the wave equation. One example is to conside acoustic

More information

c) (6) Assuming the tires do not skid, what coefficient of static friction between tires and pavement is needed?

c) (6) Assuming the tires do not skid, what coefficient of static friction between tires and pavement is needed? Geneal Physics I Exam 2 - Chs. 4,5,6 - Foces, Cicula Motion, Enegy Oct. 10, 2012 Name Rec. Inst. Rec. Time Fo full cedit, make you wok clea to the gade. Show fomulas used, essential steps, and esults with

More information

Chapter 4. Newton s Laws of Motion. Newton s Law of Motion. Sir Isaac Newton ( ) published in 1687

Chapter 4. Newton s Laws of Motion. Newton s Law of Motion. Sir Isaac Newton ( ) published in 1687 Chapte 4 Newton s Laws of Motion 1 Newton s Law of Motion Si Isaac Newton (1642 1727) published in 1687 2 1 Kinematics vs. Dynamics So fa, we discussed kinematics (chaptes 2 and 3) The discussion, was

More information

Chapter 13 Gravitation

Chapter 13 Gravitation Chapte 13 Gavitation In this chapte we will exploe the following topics: -Newton s law of gavitation, which descibes the attactive foce between two point masses and its application to extended objects

More information

Electromagnetic Waves

Electromagnetic Waves Chapte 32 Electomagnetic Waves PowePoint Lectues fo Univesity Physics, Twelfth Edition Hugh D. Young and Roge A. Feedman Lectues by James Pazun Modified P. Lam 8_11_2008 Topics fo Chapte 32 Maxwell s equations

More information

Rotational Motion: Statics and Dynamics

Rotational Motion: Statics and Dynamics Physics 07 Lectue 17 Goals: Lectue 17 Chapte 1 Define cente of mass Analyze olling motion Intoduce and analyze toque Undestand the equilibium dynamics of an extended object in esponse to foces Employ consevation

More information

Between any two masses, there exists a mutual attractive force.

Between any two masses, there exists a mutual attractive force. YEAR 12 PHYSICS: GRAVITATION PAST EXAM QUESTIONS Name: QUESTION 1 (1995 EXAM) (a) State Newton s Univesal Law of Gavitation in wods Between any two masses, thee exists a mutual attactive foce. This foce

More information

Physics 1114: Unit 5 Hand-out Homework (Answers)

Physics 1114: Unit 5 Hand-out Homework (Answers) Physics 1114: Unit 5 Hand-out Homewok (Answes) Poblem set 1 1. The flywheel on an expeimental bus is otating at 420 RPM (evolutions pe minute). To find (a) the angula velocity in ad/s (adians/second),

More information

Inverse Square Law and Polarization

Inverse Square Law and Polarization Invese Squae Law and Polaization Objectives: To show that light intensity is invesely popotional to the squae of the distance fom a point light souce and to show that the intensity of the light tansmitted

More information

Math Section 4.2 Radians, Arc Length, and Area of a Sector

Math Section 4.2 Radians, Arc Length, and Area of a Sector Math 1330 - Section 4. Radians, Ac Length, and Aea of a Secto The wod tigonomety comes fom two Geek oots, tigonon, meaning having thee sides, and mete, meaning measue. We have aleady defined the six basic

More information

Chapter 5 Force and Motion

Chapter 5 Force and Motion Chapte 5 Foce and Motion In chaptes 2 and 4 we have studied kinematics i.e. descibed the motion of objects using paametes such as the position vecto, velocity and acceleation without any insights as to

More information

COLLISIONLESS PLASMA PHYSICS TAKE-HOME EXAM

COLLISIONLESS PLASMA PHYSICS TAKE-HOME EXAM Honou School of Mathematical and Theoetical Physics Pat C Maste of Science in Mathematical and Theoetical Physics COLLISIONLESS PLASMA PHYSICS TAKE-HOME EXAM HILARY TERM 18 TUESDAY, 13TH MARCH 18, 1noon

More information

Movie Review Part One due Tuesday (in class) please print

Movie Review Part One due Tuesday (in class) please print Movie Review Pat One due Tuesday (in class) please pint Test in class on Fiday. You may stat at 8:30 if you want. (The topic of powe is not on test.) Chaptes 4-6 Main Ideas in Class Today Afte class, you

More information

Lecture 2 Date:

Lecture 2 Date: Lectue 2 Date: 5.1.217 Definition of Some TL Paametes Examples of Tansmission Lines Tansmission Lines (contd.) Fo a lossless tansmission line the second ode diffeential equation fo phasos ae: LC 2 d I

More information

b) (5) What is the magnitude of the force on the 6.0-kg block due to the contact with the 12.0-kg block?

b) (5) What is the magnitude of the force on the 6.0-kg block due to the contact with the 12.0-kg block? Geneal Physics I Exam 2 - Chs. 4,5,6 - Foces, Cicula Motion, Enegy Oct. 13, 2010 Name Rec. Inst. Rec. Time Fo full cedit, make you wok clea to the gade. Show fomulas used, essential steps, and esults with

More information

PHYS 1114, Lecture 21, March 6 Contents:

PHYS 1114, Lecture 21, March 6 Contents: PHYS 1114, Lectue 21, Mach 6 Contents: 1 This class is o cially cancelled, being eplaced by the common exam Tuesday, Mach 7, 5:30 PM. A eview and Q&A session is scheduled instead duing class time. 2 Exam

More information

Physics 1C Fall 2011: Quiz 1 Version A 1

Physics 1C Fall 2011: Quiz 1 Version A 1 Physics 1C Fall 2011: Quiz 1 Vesion A 1 Depatment of Physics Physics 1C Fall Quate - 2011 D. Mak Paddock INSTRUCTIONS: 1. Pint you full name below LAST NAME FIRST NAME MIDDLE INITIAL 2. You code numbe

More information

Uniform Circular Motion

Uniform Circular Motion Unifom Cicula Motion constant speed Pick a point in the objects motion... What diection is the velocity? HINT Think about what diection the object would tavel if the sting wee cut Unifom Cicula Motion

More information

3.2 Centripetal Acceleration

3.2 Centripetal Acceleration unifom cicula motion the motion of an object with onstant speed along a cicula path of constant adius 3.2 Centipetal Acceleation The hamme thow is a tack-and-field event in which an athlete thows a hamme

More information

ME 3600 Control Systems Frequency Domain Analysis

ME 3600 Control Systems Frequency Domain Analysis ME 3600 Contol Systems Fequency Domain Analysis The fequency esponse of a system is defined as the steady-state esponse of the system to a sinusoidal (hamonic) input. Fo linea systems, the esulting steady-state

More information

The Analysis of the Influence of the Independent Suspension on the Comfort for a Mine Truck

The Analysis of the Influence of the Independent Suspension on the Comfort for a Mine Truck 16 3 d Intenational Confeence on Vehicle, Mechanical and Electical Engineeing (ICVMEE 16 ISBN: 978-1-6595-37- The Analyi of the Influence of the Independent Supenion on the Comfot fo a Mine Tuck JINGMING

More information

AP-C WEP. h. Students should be able to recognize and solve problems that call for application both of conservation of energy and Newton s Laws.

AP-C WEP. h. Students should be able to recognize and solve problems that call for application both of conservation of energy and Newton s Laws. AP-C WEP 1. Wok a. Calculate the wok done by a specified constant foce on an object that undegoes a specified displacement. b. Relate the wok done by a foce to the aea unde a gaph of foce as a function

More information

Rotational Kinetic Energy

Rotational Kinetic Energy Add Impotant Rotational Kinetic Enegy Page: 353 NGSS Standad: N/A Rotational Kinetic Enegy MA Cuiculum Famewok (006):.1,.,.3 AP Phyic 1 Leaning Objective: N/A, but olling poblem have appeaed on peviou

More information

Force & Motion: Newton s Laws

Force & Motion: Newton s Laws oce & otion: Newton Law ( t Law) If no net foce act on a body then the body velocity cannot change. Zeo net foce implie zeo acceleation. The ma of an object detemine how difficult it i to change the object

More information

Impulse and Momentum

Impulse and Momentum Impule and Momentum 1. A ca poee 20,000 unit of momentum. What would be the ca' new momentum if... A. it elocity wee doubled. B. it elocity wee tipled. C. it ma wee doubled (by adding moe paenge and a

More information

Chapter 5 Force and Motion

Chapter 5 Force and Motion Chapte 5 Foce and Motion In Chaptes 2 and 4 we have studied kinematics, i.e., we descibed the motion of objects using paametes such as the position vecto, velocity, and acceleation without any insights

More information

PS113 Chapter 5 Dynamics of Uniform Circular Motion

PS113 Chapter 5 Dynamics of Uniform Circular Motion PS113 Chapte 5 Dynamics of Unifom Cicula Motion 1 Unifom cicula motion Unifom cicula motion is the motion of an object taveling at a constant (unifom) speed on a cicula path. The peiod T is the time equied

More information

Kinematics in 2-D (II)

Kinematics in 2-D (II) Kinematics in 2-D (II) Unifom cicula motion Tangential and adial components of Relative velocity and acceleation a Seway and Jewett 4.4 to 4.6 Pactice Poblems: Chapte 4, Objective Questions 5, 11 Chapte

More information

6.4 Period and Frequency for Uniform Circular Motion

6.4 Period and Frequency for Uniform Circular Motion 6.4 Peiod and Fequency fo Unifom Cicula Motion If the object is constained to move in a cicle and the total tangential foce acting on the total object is zeo, F θ = 0, then (Newton s Second Law), the tangential

More information

Chapter 23: GAUSS LAW 343

Chapter 23: GAUSS LAW 343 Chapte 23: GAUSS LAW 1 A total chage of 63 10 8 C is distibuted unifomly thoughout a 27-cm adius sphee The volume chage density is: A 37 10 7 C/m 3 B 69 10 6 C/m 3 C 69 10 6 C/m 2 D 25 10 4 C/m 3 76 10

More information

- 5 - TEST 1R. This is the repeat version of TEST 1, which was held during Session.

- 5 - TEST 1R. This is the repeat version of TEST 1, which was held during Session. - 5 - TEST 1R This is the epeat vesion of TEST 1, which was held duing Session. This epeat test should be attempted by those students who missed Test 1, o who wish to impove thei mak in Test 1. IF YOU

More information

Analytical calculation of the power dissipated in the LHC liner. Stefano De Santis - LBNL and Andrea Mostacci - CERN

Analytical calculation of the power dissipated in the LHC liner. Stefano De Santis - LBNL and Andrea Mostacci - CERN Analytical calculation of the powe dissipated in the LHC line Stefano De Santis - LBNL and Andea Mostacci - CERN Contents What is the Modified Bethe s Diffaction Theoy? Some inteesting consequences of

More information

Calculate the electric potential at B d2=4 m Calculate the electric potential at A d1=3 m 3 m 3 m

Calculate the electric potential at B d2=4 m Calculate the electric potential at A d1=3 m 3 m 3 m MTE : Ch 13 5:3-7pm on Oct 31 ltenate Exams: Wed Ch 13 6:3pm-8:pm (people attending the altenate exam will not be allowed to go out of the oom while othes fom pevious exam ae still aound) Thu @ 9:-1:3

More information

SPH4U Magnetism Test Name: Solutions

SPH4U Magnetism Test Name: Solutions SPH4U Magneti et Nae: Solution QUESION 1 [4 Mak] hi and the following two quetion petain to the diaga below howing two cuent-caying wie. wo cuent ae flowing in the ae diection (out of the page) a hown.

More information

Momentum is conserved if no external force

Momentum is conserved if no external force Goals: Lectue 13 Chapte 9 v Employ consevation of momentum in 1 D & 2D v Examine foces ove time (aka Impulse) Chapte 10 v Undestand the elationship between motion and enegy Assignments: l HW5, due tomoow

More information

Magnetic Dipoles Challenge Problem Solutions

Magnetic Dipoles Challenge Problem Solutions Magnetic Dipoles Challenge Poblem Solutions Poblem 1: Cicle the coect answe. Conside a tiangula loop of wie with sides a and b. The loop caies a cuent I in the diection shown, and is placed in a unifom

More information

Gauss Law. Physics 231 Lecture 2-1

Gauss Law. Physics 231 Lecture 2-1 Gauss Law Physics 31 Lectue -1 lectic Field Lines The numbe of field lines, also known as lines of foce, ae elated to stength of the electic field Moe appopiately it is the numbe of field lines cossing

More information

06 - ROTATIONAL MOTION Page 1 ( Answers at the end of all questions )

06 - ROTATIONAL MOTION Page 1 ( Answers at the end of all questions ) 06 - ROTATIONAL MOTION Page ) A body A of mass M while falling vetically downwads unde gavity beaks into two pats, a body B of mass ( / ) M and a body C of mass ( / ) M. The cente of mass of bodies B and

More information

Circular motion. Objectives. Physics terms. Assessment. Equations 5/22/14. Describe the accelerated motion of objects moving in circles.

Circular motion. Objectives. Physics terms. Assessment. Equations 5/22/14. Describe the accelerated motion of objects moving in circles. Cicula motion Objectives Descibe the acceleated motion of objects moving in cicles. Use equations to analyze the acceleated motion of objects moving in cicles.. Descibe in you own wods what this equation

More information

DYNAMICS OF UNIFORM CIRCULAR MOTION

DYNAMICS OF UNIFORM CIRCULAR MOTION Chapte 5 Dynamics of Unifom Cicula Motion Chapte 5 DYNAMICS OF UNIFOM CICULA MOTION PEVIEW An object which is moing in a cicula path with a constant speed is said to be in unifom cicula motion. Fo an object

More information