Physics formula sheet test 3

# Physics formula sheet test 3 - 1 ET=IG mzwn ar 6=So wot 3at...

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Unformatted text preview: 1 ; ET=IG mzwn+ar 6=So+wot+3at 2 2 ct) =64, +2ﬂlt9- oluzrw n; 2mm” :rnf 1-19 9 a 1 a 1 P . __......_ a=rlaf+ag =wl(?‘€l’)‘+(fﬂ?'):W=T-S ‘7“ A; 10:37:10 r=Fur”=rt’5"-r'-.'s.lngt'l2FI -r Rotational kinetic energy: K = (lf2)1w", Gravrtational potential energy: UR = mgycm Moment of inertia — Special eases: LP! ﬂ (1) Slender rod (mass = Mend length : L) pivoted at the center: I: ML2/12 Kw (2) Slender rod (mass = Mand length = L) pivoted at the end: I: MLZB AFT—":10" “ (3) Circular disk or cylinder (mass = Mand radius = R) pivoted at the center: 1= MR2}? ® (4) A point mass Mof negligible size: I= Mrz, r = distance from the pivot to the particle 85‘1” _ Parallel—axisjmeorern: 10 :_ 1m + mail, dA: distance hetweenthe pivqt point 0 and cm. Example 1. A heavy sphere with mass M is attached to the end ofa slender rod with mass rrr and length L. The rod. is pivoted at one end 0 and released from rest in the position shown. The size ofthe sphere is negligible compared with the length ofthe rod. Find the initial angular acceleration ofthe red at the instant it is released. Tint—wron— f, A. rigs-45.13 i 5 42455 : - M ' row ail 2; ;(:459)+HJ(LOI;9) 0'4 ’9“;sz «VI/4 : r* 5 p M r 9 m’ L I : 3;] m L 1 ﬂ£:,_ewwu___ ., _ L” AW ,1 m l l'“jéitmwhl’lj[Leag):émt1+mm)4/ 4i" 0 _ We ,, __ 1 A J ‘ //_\ 2. A block of mass Mis attached to a cable that wraps around the pulley as shown. The pulley is pivoted at its center, and it has radius R and moment of inertia I. The block is released from rest on the ramp, and the coefficient of friction is M between the block and the ramp. Find the acceleration of the block and the tension in the cable/ 25%) r N=rljﬁosé 57 ‘Fl‘ :ﬂkﬂjsz ' 2F: =m0w ﬂjnhe-Tvﬁiglﬁjww : M'aL ”(7') _ .. 5.7;:‘vl—R '. Q:O\[MllfQ-erdﬂf ﬂ TEzJK—C1},:ﬁ0tr=ﬁo< 4(5) V J: we #772273 e T: (5)1 Al 3. Two blocks A and B are connected by a massless cable over a pulley as shown. The radius ofthe pulley is R and it can be treated as a disk. The blocks are released from rest on the frictionless ramps. Find the accelerations of the blocks and tensions in the cable. fl) 5F; :mﬂy B) EFX : M0“ _ pm,“ 9a *2; = on» g—mjwea: mud—(2) “21 m” Mllj 1f? gem H TIE—Tia =(imﬂd “(9) 4 [3 a z 12 (Kat/‘1) Example 1, A sphere with negligible size is attached to the end of a slender red as shown. The rod is pivoted at end 0, and the assembly is released from rest at an angle 6 up from the horizontal direction. Find the speed of the sphere when the assembly swings down to the vertical position. y”. My =l£3'+%‘_ 0 I<t= i{%mLL+:—ML9‘)CJL ‘ up “yto‘ss => “in" mutenelmjétwd 1*; “i0 l‘jw M5(é’)+i\lji3‘l'> an m h is H 2L4, ed at _ _ new.» 5(3 is) ggtngtmajwatﬁghting) m 3. Two blocks A and l ire cInnected by a cable IVCI a pulley as shown. The system is released with an initial speed on for block A clown the ramp. The radius of the pulley is R and it can be treated as a disk. Find the velocity of the blocks aﬁer A slides a distance :1 along the incline. (iota. try): 4 wk; ,- Vii (151+ “A L "LOW/“1M0 vﬁ+ ilk MP2“) be} + Wis 5i ‘lﬁ‘wt leﬁgwsa d I it (ml-mm“ + ﬁg. Mpllle/Jg‘ +Wiajﬁlohbl3 a ﬂip -ﬂfcg ”‘83 £393 Ki‘il/ijffl/lt; ‘L who: : (23:; “53+an Meg: Mcr’tszvugNSr’ti" , 42/wa Mmﬁm! A w w 14/“ W‘s/r , a”, My»? V. V,_L. Y" r: dashes ‘IQ’IT'V‘ WSW". 75' L = I a; a 5:4,, (0 1:915 = 124“} (a) ﬁollfsivn ‘ mVr=Icg :75Iizok __ myr21togmgar => 8mm . e - z (52-) éav—Loéaelt (‘1) jp'i’lmoagk if , 9K— _. jurgw-e_:7 {fr/5.71 - p _ Mom e rod-n.4, some 7% were” 7, T 3 71:32 125, . F 1:: F7 "6" l 1x211: .4/ W. ’0: We l Pom}, P-ﬁé‘e ...
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