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Pengertian Polar dan nonpolar

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The indoor garden By
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The indoor garden By INDOOR GARDENS - The Classroom Victory Garden Project The Classroom Victory Garden Project Classroom Gardening Instructions Easy-Cheesy Pesto Recipe 2 cups fresh basil leaves, washed and dried 4h/n Indoor Gardening and Plant Selection Indoor Gardening 4h/n Artificial Lighting, Terrariums, Hanging Baskets, and Plant Selection UNITED HOMESTATES DEPARTMENT OF AGRICULTURE AND GARDEN BULLETIN Indoor Garden - Gare Indoor Garden October 2003 by Dona Marrier STEP 1 -Apply 3 generous coats of Polar Bear to the inside portion of the rectangle platter, using the size Me and My Job - ID Me and My Job Ian Drummond, creative director, Indoor Garden Design, London What is your typical day? I have no set working hours but generally start in the office at around 8.30am to AHL Indoor Garden Guide AHL’S Indoor Garden Guide WHAT’S INSIDE–– INDOOR LIGHTING Fluorescent Lights High Intensity DIscharge (HID) Lights Metal Halide High Pressure Sodium HGIC User's Guide - LANDSCAPE, GARDEN & INDOOR PLANTS Home & Garden . Information Center . User’s Guide . Call toll-free in South Carolina . 1-888-656-9988 . http://www.clemson.edu/hgic HGIC 1006 Bradford Pear Specifications - Indoor Gardening Supplies Hydrofarm T-5 Designer Fixture Instructions Parts: • T-5 Fluorescent fixture…………………………..x 1ea. • T-5 Bulbs (depending on model)………………...x 2, 4, 6, or 8ea. INDOOR GARDEN DESIGN PREFERRED METHODS OF PEST AND DISEASE ... INDOOR GARDEN DESIGN INDOOR GARDEN DESIGN PREFERRED METHODS OF PEST AND DISEASE CONTROL PREFERRED METHODS OF PEST AND DISEASE CONTROL The aim is to use biological control, using predatory mites or...

Kunci Jawaban Soal Essai Paket A.pdf

Kunci jawaban Babak FINAL Jenis soal : ESSAY 1. Kinerja bensin diukur berdasarkan nilai oktan (octane number) yaitu keberadaan senyawa 2,2,4 - trimetil pentane (isooktana) dengan nilai oktan 100, sedangkan nheptana nilai oktannya adalah nol. a. Gambarkan struktur 2,2,4 – trimetil pentane dan n – heptana (20 Point) Penyelesaian : b. Gambarkan semua isomer struktur n-heptana dan namai secara IUPAC (30 Point) Penyelesaian : c. Gambarkan struktur dan nama IUPAC alkena paling sederhana yang mempunyai isomer cis dan trans. (30 Point) Penyelesaian : d. Jelaskan pengertian bensin dengan angka oktan 75 % (20 Point) Penyelesaian : Angka oktan pada bensin ditentukan dengan adanya senyawa trimetil pentane dan nheptana dimana apabila pada bensin memiliki angka oktan 100 % maka pada besin tersebut terkandung senyawa trimetil pentane banding senyawa n-heptana yaitu 100 : 0, sehingga apabila bensin dengan angka oktan 75 % maka dalam bensin tersebut terkandung 75 % senyawa trimetil pentane dan 25 % senyawa n-heptana. 2. Reaksi : 2NOBr (g)  2NO (g) + Br2 (g) H = +16,1 kJ Diketahui : Tekanan awal NOBr = 0,65 atm. : NOBr telah terurai sebanyak 28% (Saat Kstb) (a) Tuliskan bentuk tetapan kesetimbangan, Kp. (10 poin) Penyelesaian : Kp  [p NO ] 2 [p Br2 ] [p NOBr ] 2 (b) Tentukan tekanan parsial gas NOBr, NO, dan Br2 setelah tercapai keadaan kesetimbangan. (30 poin) Penyelesaian : 100  28 p NOBr   0,65 atm  0,468 atm 100 28 p NO   0,65 atm  0,182 atm 100 p Br2  28 2 100  0,65 atm  0,091 atm (c) Tentukan tekanan total sesudai tercapai kesetimbangan (20 poin) Penyelesaian : (100  28 )  (28  14 ) 114 p tot  [ ]  0,65 atm   0,65 atm  0,741 atm 100 100 (d) Hitung nilai tetapan kesetimbangan, Kp pada temperatur tersebut. (20 poin) Penyelesaian :

NEW ARRIVAL & VEHICLE FOR SALE- MARCH 31, 2014 - PSBank

AS OF MARCH 31, 2014 # Model MAKE/MODEL 1 12 HONDA CITY 1.5E (GAS) - A/T MITSUBISHI ADVENTURE GLX 2.5 (DSL) M/T MITSUBISHI ADVENTURE GLS SPORT SE 2.5L (DSL) - M/T 2 3 4 5 6 7 8 10 12 REGULAR DISCOUNTED PLATE NO COLOR DN 3456 CRYSTAL BLACK 13,223 LAS PINAS 590,000.00 540,000.00 531,000.00 486,000.00 FHH-904 DOMINIC SILVER 82,239 BACOLOD 450,000.00 410,000.00 405,000.00 369,000.00 UUI-593 ORION BLACK 14,423 SAN JUAN 630,000.00 570,000.00 567,000.00 513,000.00 MILEAGE (KMS) REGISTERED IN SELLING PRICE FLOOR PRICE SELLING PRICE FLOOR PRICE 11 MITSUBISHI LANCER GLS 1.6 (GAS) - A/T VFB-270 PYRENESE BLACK 14,899 LTO KAWIT 510,000.00 460,000.00 459,000.00 414,000.00 13 SUZUKI ALTO 800 STD (GAS) - M/T UB 0903 S,WHITE 9,998 PASAY CITY 310,000.00 280,000.00 279,000.00 252,000.00 13 TOYOTA FORTUNER 2.5L G (DSL) - M/T TV 7169 BLACK 7,597 MANILA NORTH 1,050,000.00 950,000.00 945,000.00 855,000.00 13 13 TOYOTA INNOVA 2.5E (DSL) - A/T TOYOTA VIOS 1.3G (GAS) - M/T UQG-509 UJQ-118 BRONZE MICA MET THERMALYTE 7,048 19,165 MANILA WEST MARIKINA 770,000.00 540,000.00 700,000.00 490,000.00 693,000.00 486,000.00 630,000.00 441,000.00 www.psbank.com.ph Tel. nos.: 514-2461 and 514-2463 Fax No.: 633-0533 ========================= Units are available for viewing: Monday - Saturday 8:30 am - 5:00 pm 128 Sun Valley Drive, Km. 15, West Service Road, South Superhighway, Parañaque City Documents Classification: PUBLIC VEHICLES FOR SALE AS OF MARCH 31, 2014 # 1 2 3 MAKE/MODEL Model PLATE NO COLOR MILEAGE (KMS) REGISTERED IN DISCOUNTED SELLING PRICE FLOOR PRICE 09 CHEVROLET AVEO 1.2L HATCHBACK (GAS) - M/T NEI-354 GALAXY WHITE 53,099 CAMP AGUINALDO 330,000.00 300,000.00 297,000.00 270,000.00 10 CHEVROLET CRUZE LS 1.8L (GAS) - A/T PRO-234 GALAXY WHITE 43,985 LA LOMA 580,000.00 530,000.00 522,000.00 477,000.00 CHEVROLET CRUZE LS 1.8L (GAS) - A/T PVQ-669 SUPER RED LA LOMA 540,000.00 490,000.00 486,000.00 441,000.00 10 4 11 5 13 CHEVROLET CRUZE 1.8L DVVT (GAS) M/T CHEVROLET CRUZE 1.8L (GAS) - M/T 6 12 CHEVROLET TRAVERSE (GAS) - A/T 7 8 09 10 FORD ESCAPE XLS 2.3L (GAS) - A/T FORD ESCAPE 2.3L XLS - A/T 9 10 11 12 POB-393 PEWTER GRAY UFO-889 NO PLATE (WA 5994) NGO-345 NIU-125 CARBON FLASHMET INFRA RED BLUE 50,764 101,443 FORD ESCAPE XLS 2.3L (GAS) - A/T VFE-310 PANTHER BLACK FORD ESCAPE XLS 2.3L (GAS) - A/T TGO-750 CHILL 11 12 13 14 15 16 17 12 FORD ESCAPE XLT 2.3L (GAS) - A/T NO PLATE (JD 6351) TONIC (BABY BLUE) 12 13 13 13 10 11 FORD FORD FORD FORD FORD FORD UQG-633 JD 7734 UWO-843 UQE-932 PLQ-926 VFD-425 WHITE DIAMOND WHITE PANTHER BLACK PANTHER BLACK COOL WHITE BLACK 18 11 FORD EVEREST ICE (DSL) - A/T POW-486 19 20 21 22 23 24 25 26 27 12 12 13 13 13 11 11 12 12 FORD FORD FORD FORD FORD FORD FORD FORD FORD VFF-831 UXI-579 KGN-603 UQE-572 WDO-353 TOI-830 PIJ-470 UQF-865 LHC-152 28 12 FORD FIESTA TREND HB 1.6 (GAS) - A/T 12 FORD FIESTA TREND HACTHBACK 1.4L A/T 30 12 31 32 33 34 13 13 13 13 29 REGULAR SELLING PRICE FLOOR PRICE 9,661 560,000.00 510,000.00 504,000.00 459,000.00 TAGUIG 650,000.00 590,000.00 585,000.00 531,000.00 TAGUIG 2,060,000.00 1,860,000.00 1,854,000.00 1,674,000.00 600,000.00 590,000.00 540,000.00 540,000.00 540,000.00 531,000.00 486,000.00 486,000.00 66,466 CALAMBA 640,000.00 580,000.00 576,000.00 522,000.00 23,367 NAVOTAS 760,000.00 690,000.00 684,000.00 621,000.00 38,923 MUNTINLUPA 750,000.00 680,000.00 675,000.00 612,000.00 29,453 20,826 30,644 6,268 51,834 60,417 MANILA WEST NOVALICHES NOVALICHES NOVALICHES MANILA NORTH SAN PABLO CITY 730,000.00 800,000.00 770,000.00 820,000.00 880,000.00 860,000.00 660,000.00 720,000.00 700,000.00 740,000.00 800,000.00 780,000.00 657,000.00 720,000.00 693,000.00 738,000.00 792,000.00 774,000.00 594,000.00 648,000.00 630,000.00 666,000.00 720,000.00 702,000.00 H.LIGHT SILVER 60,046 MANILA NORTH WHITE GRAY GRAY COOL WHITE BLACK COOL WHITE COOL WHITE BLACK MICA 39,778 27,676 5,142 39,778 22,326 24,637 32,293 16,082 28,703 CALAMBA TAGBILARAN PUERTO EXTENSION NOVALICHES LAS PINAS MANILA NORTH QUEZON CITY MUNTINLUPA DAVAO CITY VEN-370 BLACK 45,688 TQA-904 TRUE RED FORD FIESTA SPORT HB (GAS) - A/T UQF-122 FORD FORD FORD FORD IE 4053 UOU-152 WWO-955 UTQ-597 EVEREST LTD ICE - A/T EVEREST 2.5L - M/T EVEREST 2.5 (DSL) - A/T EVEREST 2.5 (DSL) - A/T EVEREST 2.5L TDCI (DSL) - A/T FIESTA 1.6L (GAS) - A/T FIESTA 1.4L (GAS) - M/T FIESTA 1.4L (GAS) - A/T FIESTA TREND 1.6L (GAS) - A/T FIESTA FIESTA FIESTA FIESTA TREND 1.6L (GAS) - A/T TREND 1.6 (GAS) - A/T TREND 1.6L (GAS) - A/T 1.6L SPORT (GAS) - A/T 38,607 QUEZON CITY MANILA WEST VALENZUELA ESCAPE XLS 2.3L - A/T ESCAPE XLS 2.3L (GAS) - A/T ESCAPE XLS 2.3L (GAS) - A/T ESCAPE XLT 2.3L (GAS) - A/T EVEREST 2.5 TDCI (DSL) - A/T EVEREST XLT 2.5L (DSL) - M/T BLACK GRANITE M. 40,698 960,000.00 870,000.00 864,000.00 783,000.00 1,030,000.00 970,000.00 1,160,000.00 1,120,000.00 1,120,000.00 510,000.00 500,000.00 590,000.00 550,000.00 930,000.00 880,000.00 1,050,000.00 1,010,000.00 1,010,000.00 460,000.00 450,000.00 540,000.00 500,000.00 927,000.00 873,000.00 1,044,000.00 1,008,000.00 1,008,000.00 459,000.00 450,000.00 531,000.00 450,000.00 837,000.00 792,000.00 945,000.00 909,000.00 909,000.00 414,000.00 405,000.00 486,000.00 405,000.00 BATANGAS 550,000.00 500,000.00 450,000.00 405,000.00 8,668 QUEZON CITY 590,000.00 540,000.00 531,000.00 486,000.00 POLAR WHITE 14,912 MUNTINLUPA 600,000.00 540,000.00 540,000.00 486,000.00 H. SILVER ICE BLUE ICY BLUE AURORA BLUE 23,015 7,735 8,010 25,200 NAVOTAS MANILA NORTH NOVALICHES MUNTINLUPA 570,000.00 600,000.00 600,000.00 610,000.00 520,000.00 540,000.00 540,000.00 550,000.00 513,000.00 540,000.00 540,000.00 549,000.00 468,000.00 486,000.00 486,000.00 495,000.00 35 13 FORD FIESTA 1.6L (GAS) - A/T WWO-983 SPARKLING GOLD NOVALICHES 610,000.00 550,000.00 549,000.00 495,000.00 36 08 FORD FOCUS 1.8 (GAS) - M/T ZRU-130 GOLD

Panduan penulisan Penerbitan Buku Teks - PDPT

Panduan Penulisan Buku Panduan ini merupakan petunjuk penulisan buku pelajaran (ilmiah populer) yang digunakan untuk menentukan kelayakan naskah bagi penerbit. Panduan ini membahas pengertian buku pelajaran & diktat, tujuan penulisan buku pelajaran, isi buku pelajaran, sampul buku, bagian pembuka, bagian utama dan bagian penutup serta ketentuan jumlah halaman. Buku Pelajaran (Text book) & Diktat Buku pelajaran adalah bahan/materi pelajaran yang dituangkan secara tertulis dalam bentuk buku dan digunakan sebagai bahan pelajaran (sumber informasi) sebuah mata kuliah bagi mahasiswa dan pengajar susuai dengan kebutuhan lapangan/industry dan tuntutan perkembangan teknologi dan atau kurikulum. Diktat adalah catatan tertulis suatu bidang studi yang disiapkan oleh guru/dosen untuk mempermudah pengayaan materi pelajaran atau bidang studi yang dibahas dalam proses pembelajaran (Ilvandri, 2011). Diktat yang baik merupakan draft buku ajar yang belum diterbitkan. Tujuan penulisan buku pelajaran a. Menyediakan buku susuai dengan kebutuhan mahasiswa, institusi dan lapangan/ industry serta serta tuntutan perkembangan teknologi atau kurikulum. b. Mendorong penulis/dosen untuk berkreasi dan kreatif membagikan ilmunya kepada masyarakat. c. Mendorong penulis untuk meng-update ilmunya sesuai dengan kriteria tuntutan buku layak terbit mencakup subdstansi, bahasa dan potensi pasar. d. Mendukung penulis untuk menerbitkan buku bila belum terbit. Isi Buku Pelajaran Isi buku pelajaran berupa teori, konsep, formula atau aturan terkini dilengkapi dengan contoh-contoh masalah atau studi kasus serta solusinya. Isi buku harus orsinil dengan merujuk dari berbagai sumber. Informasi tepat, dapat dipercaya dan dipertanggungjawabkan kepada pembaca dan semua pihak terkait. Isi tersusun dengan baik atau dengan alur informasi yang mudah dipahami. Buku pelajaran dan diktat yang baik memenuhi tiga aspek pendidikan yaitu ilmu pengetahuan (knowledge), keterampilan (skills) dan sikap atau perilaku (attitude). Aspek tersebut seperti yang dinyatakan oleh UNESCO (1994) yaitu...

hulk vs. the abomination. ang lee's arthouse ... - Nick de Semlyen

Visa Inc. has teamed up with Marvel Comics to create a new financial literacy ... ...education, this unique partnership features Spider-Man, Iron Man, Thor, Hulk ... and energetic Frenchman who, as a young boy, marvelled at Bruce — or rather, ‘David’ — Banner’s small-screen adventures. After hearing about the project at a meeting with Marvel, the director of the two Transporter films flew home to Paris and worked with a graphic artist friend to create a series of illustrations, which he sent to the studio. Not long after, he was offered the job. Visiting Leterrier at Hulk HQ, a building complex in West LA that also houses production offices for Iron Man and Transformers 2, Empire gets a first-hand look at the paintings, which are spectacular, cinematic and gloriously over-the-top. One portrays Hulk grappling with not one, not two, but six polar bears; in another the gamma freak trashes an NYPD squad car; while a third shows Hulk squatting beneath a moonlit Central Park bridge, as oblivious passers-by stroll above. Between them they showcase all the potential — from comedy to tragedy to pulse-pounding excitement — inherent in the character. Leterrier’s office is littered with more toys than Harry Knowles’ basement: Hulk hands sit alongside towers of comics and prototype action figures for the new movie. Even after two years of 18-hour days and endless debates over details as minor as whether Bruce Banner wears jeans or chinos, the director’s enthusiasm for big green lunks in

The Corliss Group Travelers Scandinavia travel guide

An essential guide to Scandinavia, including information on Sweden, Norway and Denmark, attractions, transport, when to go, where to stay and top travel tips. By Andrew Stone, our Scandinavia expert. The word “Scandinavia” evokes many images. Endless fir forests, awe-inspiring fjords, wilderness, and lately, perhaps, crime fiction and noir thrillers such as Borgen, Wallander and The Killing. It’s all these things, of course, but this hardly does justice to the region’s vastness and diversity. To the North is the Arctic Circle, where polar bears roam, the summer sun lasts 24 hours, but an implacable dark descends in a winter lit, if you’re lucky, by cosmic northern lights. Although not in Scandinavia, Finland, where Russia's cultural orbit is felt, also has a Nordic feel with vast expanses of lake and forest inhabited by wild bears stretch beyond sight. Nomadic reindeer herders range from mountain to forest and the naked sauna is a national pastime.

Nike + iPod User Guide - Support - Apple

© 2011 Apple Inc. All rights reserved. Apple, the Apple logo, iPhone, iPod, iPod nano, iPod touch, and iTunes are trademarks of Apple Inc., registered in the U.S. and other countries. Shuffle is a trademark of Apple Inc. iTunes Store is a service mark of Apple Inc., registered in the U.S. and other countries. NIKE and the Swoosh Design are trademarks of NIKE, Inc. and its affiliates, and are used under license. The Nike + iPod Sport Kit is covered by one or more of U.S. patent numbers 6,018,705, 6,052,654, 6,493,652, 6,298,314, 6,611,789, 6,876,947, and 6,882,955, either alone or when used in combination with a Nike + iPod enabled iPod media player or iPhone. Polar Wearlink is a trademark of Polar, Inc. Mention of third-party products is for informational purposes only and constitutes neither an endorsement nor a recommendation. Apple assumes no responsibility with regard to the performance or use of these products. All understandings, agreements, or warranties, if any, take place directly between the vendors and the prospective users. Every effort has been made to ensure that the information in this manual is accurate. Apple is not responsible for printing or clerical errors. Your Personal Workout Assistant Nike + iPod is a workout partner and coach all in one. Select the type of workout you want—open-ended, distance, time, or calorie-burning—choose music to keep you motivated, and then keep track of your progress every step of the way with spoken and onscreen feedback. Upload your workout data to nikeplus.com, where you can set goals and monitor your improvement from workout to workout. Join the world’s largest online running community, participating in challenges with runners from across the globe. Nike + iPod is supported by iPhone (3GS or later), all iPod nano models1, and iPod touch (2nd generation or later).

AutoCAD LT 2014 brochure - ACE-Hellas
by nami 0 Comments favorite 15 Viewed Download 0 Times

Speed design with Autodesk AutoCAD LT 2014 Design with precision and share your work confidently with the unmatched assurance of TrustedDWG technology What’s new • A more intelligent command line reduces repetitive tasks • Design feed social collaboration drives stakeholder involvement Benefits • Live maps and geolocation tools incorporate real-world contexts • File tabs provide a visually intuitive way to select drawings The professional choice for 2D drafting Document 2D concepts with the connected design features of Autodesk® AutoCAD LT® drafting software. Powerful documentation tools help you create precise technical drawings you can efficiently edit, repurpose, and share with confidence. Gather feedback and collaborate on changes throughout the project lifecycle using sharing options and workflow integration from almost anywhere. • Preserve design information with TrustedDWG™ technology • Access files from almost anywhere with Autodesk® 360 Increased productivity Enhanced 2D drafting tools help you work more quickly and efficiently: • Save time with efficient tools to locate commands and view all open drawings • Create multiple design elements quickly by using rectangular, polar, and path arrays • Speed documentation by automatically creating views from your design models Maximum compatibility Files created with TrustedDWG are 100 percent compatible with other Autodesk software: • Share your designs with ease, no matter if your collaborators are using software like Autodesk® AutoCAD® or AutoCAD® 360 • Import models from a wide variety of formats and automatically generate intelligent CAD documentation • Make the move to Building Information Modeling (BIM) or 3D mechanical CAD with Autodesk® software product interoperability • Boost drafting speed with smart and intuitive user tools • Document your designs with powerful 2D detailing features Trusted reliability AutoCAD LT is built on the AutoCAD platform, used by millions of professionals for over 30 years: • Access and share your designs from mobile devices with Autodesk 360 cloud services • Read and write files from previous versions of AutoCAD and AutoCAD LT with full backward compatibility • Create drawings using the latest DWG™ technology and have confidence in data integrity when sharing your work Without AutoCAD LT, I wouldn’t be able to put everything on paper, and make sure that it all worked before going into the construction phase. –Natalie Cutler Interior Designer/Owner Cutler Design & Construction ...

The Best Alcohol and Drug Addiction Treatment-www.addictionts.com

ATS is a 6 month outpatient, medically assisted, treatment program.  We combine Cognitive Behavior Therapy with medications to assist patients achieve long lasting outcomes.  We work with patients that have had difficulty with previous recovery programs, consequently are eager to become focused on getting better.  97% of our patients complete the entire 6 months Phase I program. Phase II is an option exercised by 89 % of our patient completing the initial program.  Almost all of our patients have co-occurring mental health issues including anxiety, depression, ADHD, or bi-polar illnesses. http://www.addictionts.com

Equation Sheet for Engineering Mechanics 12—Dynamics

Equation Sheet for Engineering Mechanics 12—Dynamics Note: vectors are indicated by boldface type. Miscellaneous If ax2 + bx + c = 0, then x = −b ± √ b2 − 4ac 2a. Rectilinear (1-D) Motion Position: s(t); Velocity: v = s = ds/dt; Acceleration: a = s = dv/dt = d2 s/dt2 = vdv/dx. For ˙ ¨ constant acceleration ac : 2 v 2 = v0 + 2ac (s − s0 ) s = s0 + v0 t + 1 ac t2 2 v = v0 + ac t 2D Motions—Cartesian Coordinates Position: r = xˆ + yˆ Velocity: v = dr/dt = xˆ + yˆ Acceleration: a = dv/dt = d2 r/dt2 = xˆ + yˆ ı ; ˙ ı ˙ ; ¨ı ¨ 2D Motions—Normal-Tangential (Path) Coordinates ˙ v = ρθ v = vˆt e a = atˆt + anˆn e e ˙ an = ρθ2 = v 2 /ρ at = v ˙ 2D Motions—Polar Coordinates r = rˆr e v = vr ˆr + vθ ˆθ e e 2 ˙ ar = r − rθ ¨ a = ar ˆr + aθ ˆθ e e ˙ vθ = r θ vr = r ˙ ¨ aθ = rθ + 2rθ ˙˙ Newton’s Second Law F = ma; Fx = max ; Fy = may ; Fn = man ; Ft = mat ; Fr = mar ; Fθ = maθ Work-Energy Principle U1–2 = L F · dr Vg = W y T = 1 mv 2 2 T1 + U1–2 = T2 Ve = 1 kδ 2 2 T1 + V1 + (U1–2 )nc = T2 + V2 Linear Impulse-Momentum Principle p = mv F= dp dt t2 L1–2 = t1 F dt = mv2 − mv1 Impact of Smooth Particles For a coefficient of restitution e, in the direction along to the line of impact (LOI) or n direction: vseparate vB − vA2 e= = 2 vapproach vA1 − vB1 Total linear momentum is conserved in the n direction: (mA vA1 + mB vB1 = mA vA2 + mB vB2 )n . Velocity of each particle is conserved perpendicular to the LOI (t direction):(vA1 = vA2 )t and (vB1 = vB2 )t . Angular Impulse-Momentum Principle ˙ hO = mr2 θ ˙ MA = hA + vA × mvG hA = rP/A × mv t2 (AA )1–2 = t1 r × F dt = t2 t1 MA dt = h2 − h1 Rigid Body Kinematics vB = vA + vB/A aB = aA + aB/A vB = vA + ω × rB/A aB = aA + α × rB/A + ω × (ω × rB/A ) vB = vA + Ω × rB/A + (vB/A )xyz where xyz refers to the rotating frame (B) ˙ aB = aA + Ω × rB/A + Ω × (Ω × rB/A ) + (aB/A )xyz + 2Ω × (vB/A )xyz Moments of Inertia (IG )disk = 1 mr2 2 (IG )rod = 2 1 12 ml (IG )plate = 2 1 12 m(a + b2 ) (IG )sphere = 2 mr2 5 2 Parallel Axis Theorem: IA = IG + md2 ; Radius of Gyration: IA = mkA Angular Momentum and Equations of Motion for a Rigid Body Angular Momentum hA = IG ω + rG/A × mvG hA = IA ω + rG/A × mvA Equations of Motion MG = IG α and for a fixed point O: For the mass center G: MA = IG α + rG/A × maG MO = IO α. For an arbitrary point A: MA = IA α + rG/A × maA (MA )FBD = (MA )MAD Work-Energy for a Rigid Body The work-energy principle is the same as that for particles. The kinetic energy of a rigid body is: 2 y ¯ T = 1 mvA + 1 IA ω 2 − mω(¯vAx − xvAy ) 2 2 Vibrations Undamped free vibration: Equation of motion: x + p2 x = 0, p = k/m, x(t) = x0 cos pt + ¨ (v0 /p) sin pt. Period: τ = 2π/p. Frequency: f = 1/τ = p/2π. Damped free vibration: Equation of motion: m¨ + cx + kx = 0, ζ = c/ccr = c/(2mp), x ˙ √ √ 2 2 x(t) = A1 e(−ζ+ ζ −1)pt + A2 e(−ζ− ζ −1)pt , and for ζ < 1: x(t) = Ee−ζpt sin(ωd t + α), where E and α are constants and ωd = p 1 − ζ 2 . Harmonic Forcing: Equation of motion: x + p2 x = P0 sin ωt with solution: ¨ P0 /k x(t) = E sin(pt + α) + sin ωt 1 − (ω/p)2 Damped Forced Vibration: Equation of motion: m¨ + cx + kx = P0 sin ωt with solution: x ˙ x(t) = X sin(ωt + φ), where P0 /k X= [1 − (ω/p)2 ]2 + (2ζω/p)2 2ζω/p φ = tan−1 1 − (ω/p)2

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