9. Rotation of rigid bodies (327-360; 34) rigid

9. Rotation of rigid bodies (327-360; 34) rigid

9. Rotation of rigid bodies (327-360; 34) rigid body

radian average angular velocity angular displacement instantaneous angular velocity average angular acceleration instantaneous angular acceleration

angular speed tangential component of acceleration centripetal component of acceleration moment of inertia rotational kinetic energy parallel-axis theorem

stjarfhlutur radian (radan) mealhornhrai hornfrsla stundarhornhrai

mealhornhrun stundarhornhrun hornhrai snertilttur hrunar misknarttur hrunar hverfitrega

snningsorka setning um samhlia sa 327 328 329

329 329 331 331 336 336

336 340 340 345 Tveir blar, annar tvisvar sinnum yngri en hinn,

standa kyrrir lrttum fleti. Tveir menn jafnsterkir ta hvorum bl fyrir sig 5 s. Er skriungi lttari blsins eftir etta (engin nningsmtstaa): 1. minni en 2. jafnstr og

3. meiri en skriungi yngri blsins Tveir blar, annar tvisvar sinnum yngri en hinn, standa kyrrir lrttum fleti. Tveir menn jafnsterkir ta hvorum bl fyrir sig 5 s. Er

skriungi lttari blsins eftir etta (engin nningsmtstaa): 1. minni en 2. jafnstr og 3. meiri en skriungi yngri blsins

Atlag (Impulse) = breyting skriunga (J = p) Atlag (J = F t ) a sama bum tilvikum. Tveir blar, annar tvisvar sinnum yngri en hinn, standa kyrrir lrttum fleti. Tveir menn

jafnsterkir ta hvorum bl fyrir sig 5 s. Er hreyfiorka lttari blsins eftir etta (engin nningsmtstaa): 1. minni en 2. jafnstr og 3. meiri en

hreyfiorka yngri blsins Tveir blar, annar tvisvar sinnum yngri en hinn, standa kyrrir lrttum fleti. Tveir menn jafnsterkir ta hvorum bl fyrir sig 5 s. Er hreyfiorka lttari blsins eftir etta (engin

nningsmtstaa): 1. minni en 2. jafnstr og 3. meiri en hreyfiorka yngri blsins Af v a skriungi beggja bla er s sami hltur

hreyfiorka lttari blsins a vera meiri (v2!). Gangfri snnings 1

f Lsum snningi me horni, , en a m lka heimfra upp bogalengd, s, me jfnunni = s/r

Hornhrai er skilgreindur sem = ddt Hann er tengdur umferartma og tni me jfnunum = 2/T = 2 f

Umml hrings: 2 r Gangfri snnings 2 Einnig er hornhrainn tengdur hraa v = r

Hornhrun er = ddt = d2dt2 Jfnur um snning me fastri hornhrun eru hlistar jfnum um lnulega hreyfingu me fastri hrun a.

Hreyfing/snningur me jafnri (horn)hrun Fylgikver s. 12, Univ.Phys. s. 334 http://wps.aw.com/aw_young_physics_11

7.7 Rotational Kinematics Snningsorka og hverfitrega 1 stjarfhlut sem snst um s sem er fastur mia vi hlutinn hafa allar agnir sama hornhraa :

v i = Ri K = mi vi 2 = mi Ri 2 2 Snningsorka og hverfitrega 2

Fengum K = mi Ri 2 2 Vi tkum 2 t fyrir sviga og innleium hverfitreguna I = mi Ri 2

K = ( mi Ri 2) 2 = I 2

Ef massinn er samfellt dreifur sta agna fst heildi sta summu: I = R 2 dV A rider in a barrel of fun finds herself stuck

with her back to the wall. Which diagram correctly shows the forces acting on her? A rider in a barrel of fun finds herself stuck with her back to the wall. Which diagram correctly shows the forces acting on her?

v Hvernig var dmi um krakkana og ryggisbelti! Suppose you are sitting in a soundproof, windowless room aboard a hovercraft moving over

flat terrain. Which of the following can you detect from inside the room? 1. rotation 2. deviation from the horizontal orientation 3. motion at a steady speed 4. acceleration

5. state of rest with respect to ground Suppose you are sitting in a soundproof, windowless room aboard a hovercraft moving over flat terrain. Which of the following can you detect from inside the room?

1. rotation 2. deviation from the horizontal orientation 3. motion at a steady speed 4. acceleration 5. state of rest with respect to ground Engar mlingar geta fundi

jafna hreyfingu (ea kyrrstu), vi finnum fyrir hrun. Setningin um samsa sa (Steiner) Paralell-Axis Theorem IP = ICM + M d 2

ICM er hverfitrega (moment of inertia) hlutar um s gegnum massamijuna og IP er hverfitregan um einhvern s samsa honum. M er heildarmassinn og d er fjarlgin milli sanna.

UnivPhys s. 345 Jakob Steiner, strfringur (rmfri) Fddur: 18. mars 1796 Utzenstorf, Sviss Dinn: 1. aprl 1863 Bern, Sviss Lri ekki a lesa fyrr en hann var 14 ra

en komst samt til mikils roska. The moment of inertia of a rigid body about a fixed axis through its center of mass is I. The moment of inertia of this same body about a parallel axis through some other point is always 1. smaller than I.

2. the same as I. 3. larger than I. 4. whether its larger or smaller depends on the choice of axis The moment of inertia of a rigid body about a fixed axis through

its center of mass is I. The moment of inertia of this same body about a parallel axis through some other point is always 1. smaller than I. 2. the same as I. 3. larger than I. 4. whether its larger or smaller depends on the choice of

axis Hva sagi Steiner? Example 9.9. s. 343 Univ Phys

http://wps.aw.com/aw_young_physics_11 7.6 Rotational Inertia Estimation Video: Windmill 1 Estimation Video: Windmill 2 Mnudaga:

rijudaga: Mivikudaga: Fimmtudaga: Fstudaga: Arnar Hjartarson

rni Sigursson Einar Svarsson Silja Rn Sigurardttir Reynir Bergmann Plsson Sl llsmul:

Verkfrideild bur ykkur upp asto eldri nema vi heimaverkefni ea hvaeina sem er a vefjast fyrir ykkur varandi nmi. Er etta til vibtar hefbundnum dmatmum og er algjrlega frjls mting. Eldri nemar vera til vitals stofu 155 mnudaga, rijudaga og fimmtudaga og stofu 156 mivikudgum og fstudgum hdeginu fr 12:15-13:15. anga geti i leita og munu nemendur astoa ykkur eftir fremsta megni. anga

geti i leita me spurningar um heimadmi ea anna sem er a vefjast fyrir ykkur. Ekki er tlast til a astoarflki leysi algjrlega fyrir ykkur ll verkefni, heldur komi ykkur af sta. A sjlfsgu eigi i einnig a vera feimin vi a spyrja kennara fyrirlestrum og dmatmum. g vona a i noti ykkur etta til hins trasta og a etta gagnist ykkur. Bestu kvejur,

Sigurur Brynjlfsson forseti verkfrideildar Kraftvgi (Torque) Kraftvgi er skilgreint sem vigurinn:

=rxF = r F sin (kraftur sinnum armur) M lesa tvo vegu mynd, annars vegar sem r F og hins vegar sem r F.

You are using a wrench and trying to loosen a rusty nut. Which of the arrangements shown is most effective in loosening the nut? You are using a wrench and trying to loosen

a rusty nut. Which of the arrangements shown is most effective in loosening the nut? 2-1-4-3 Athugasemd eins nemenda:

llum myndunum er veri a hera boltann en ekki losa! =rxF = r F sin

Stjarfhlutur me hlirun og snningi A wheel rolls without slipping along a horizontal surface. The center of the wheel has a translational speed v. The lowermost point on the wheel has a net forward velocity 1. 2v

2. v 3. zero 4. need more information A disk rolls without slipping along a horizontal surface. The center of the disk has a translational speed v. The uppermost

point on the disk has a translational speed 1. 0 2. v 3. 2v 4. need more information

Hlutur fer rekst l, eitt skipti massamijuna, hitt skipti annan endann. Er hrai massamijunnar s sami bi skiptin? 1. J

2. Nei http://wps.aw.com/aw_young_physics_11 7.11 Race Between a Block and a Disk Hver kemur fyrst niur (fr vinstri til hgri)?

1. Gegnheil kla 2. Hringur 3. Gegnheill svalningur 4. Hol kla 5. Gegnheill svalningur

Hver kemur fyrst niur (fr vinstri til hgri)? 1. Gegnheil kla 1 2. Hringur 5 3. Gegnheill svalningur

2-3 4. Hol kla 4 5. Gegnheill svalningur 2-3

Tvr holar klur lta eins t, r eru jafnstrar og jafnungar og bar mlaar sama lit. nnur er hinsvegar ger r li en hin r kopar. Geti i fundi afer til a greina r sundur?

Lta r renna niur skbraut! Tvr klur nkvmlega eins hefja fer sna me sama hraa sta A. Hrainn ngir til a klan efri mynd komist yfir rskuldinn. Hvor klan nr sta B undan?

1. Klan efri mynd verur undan. 2. Klan neri mynd verur undan. 3. r eru jafnfljtar. Karlinn kassanum

Ef tir karlinum niur og sleppir honum san poppar hann upp vegna gormsins. Er hgt a rsta karlinum a langt niur a boxi fylgi honum upp lofti egar honum er sleppt? 1. J

2. Nei 3. g veit a ekki vinna unnin af kraftvgi Hverfiungi agnar er skilgreindur me

krossfeldi staarvigurs og skriunga Heildarhverfiungi stjarfhlutar er summan af hverfiunga agnanna sem mynda hann. Hverfiunginn arf ekki a liggja samsa snningssnum.

Ef hluturinn er samhverfur um snningssinn er heildarhverfiunginn samsa snum: Dmi 10.40 s. 396 Univ.Phys. Hverfitrega: hendur ti: I1 = 2,6 kgm2, hendur a brjsti: I2 = 0,9 kgm2

Hverfiungi er varveittur: I22 = I11, snningshrainn refaldast! Hvernig hefur snningsorka Einsteins breyst vi a draga lin inn? 1. Hn er s sama

2. Hn er meiri v hann snst hraar 3. Hn er minni v hverfitrega hans er minni Snningsorkan vex! Snningsorkan er I2 . Setjum inn hverfiungann, L = I,

verur snningsorkan L. Hverfiunginn er varveittur, breytist ekki, en vex, v hltur snningsorkan a aukast. Hvaan kemur essi orka? Hn kemur r vinnunni vi a draga lin a lkamanum!

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