C D o F. 30 o F. Wall String. 53 o. F y A B C D E. m 2. m 1. m a. v Merry-go round. Phy 231 Sp 03 Homework #8 Page 1 of 4

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1 Phy 231 Sp 3 Hoework #8 Pge 1 of 4 8-1) rigid squre object of negligible weight is cted upon by the forces 1 nd 2 shown t the right, which pull on its corners The forces re drwn to scle in ters of the dotted lines Which one of the lbelled forces nd loctions will produce equilibriu? () (b) (c) (d) (e) 8-2) force = 4 N is pulling on one end of stick of length = 2 bout wht re the gnitudes of the torques bout the other end of the stick (point ) when the force is pplied in the two different cses, nd shown t the right () : 4 N-; : 4 N- (b) : 8 N-; : 4 N- (c) : 7 N-; : 4 N- (d) : 4 N-; : 7 N- (e) : 7 N-, : 7 N- 3 o o unifor rod of ss 6 kg nd length = 2 is ttched to wll t one end by pivot nd t the other end by horizontl string The rod is in sttic equilibriu t n ngle of 53 o with the wll 8-3) bout wht is the gnitude of the tension T in the string? () 8 N (b) 23 N (c) 3 N (d) 6 N (e) 4 N 8-4) bout wht is the gnitude of the verticl force v on the rod t the pivot? () 6 N (b) 3 N (c) 23 N (d) 4 N (e) 9 N Wll String y 53 o T 8-5) The five figures shown t the right ll hve the se height nd re ll of unifor density Which one hs its center of grvity closest to the ground? () (b) (c) (d) (e) 8-6) Two prticles of ss 1 = 2 kg nd 2 = 6 kg, respectively, re seprted by distnce = 8 c s shown t the right How fr fro the sller ss is the center of grvity of these two sses? () 4 c (b) 2 c (c) 6 c (d) 5 c (e) 8 c 8-7) unifor solid cylinder de of led hs the se ss nd the se length s unifor solid cylinder of wood The rottionl inerti of the led cylinder (bout its cylindricl xis) copred to the wood one is: (Note: led is uch denser thn wood) () lrger (b) sller (c) the se (d) you need to know the rdii to tell (e) you need to know both the sses nd the rdii to tell 8-8) Wht is the oent of inerti I of the four equl sses shown t the right bout the xis (sticking out of the pge) t the center of the four sses? () 2 2 (b) 6 2 (c) 2 (d) 4 2 (e) None of these is right ) disk of rottionl inerti I, initilly rotting with ngulr speed ω stops in tie t due to retrding torque τ If the torque is doubled, nd the initil ngulr speed is hlved, bout how long should it tke for the disk to stop? () t /4 (b) t /2 (c) t (d) 2t (e) 4t 8-1) disk of rottionl inerti I, initilly rotting with ngulr speed ω oves through n ngle ϑ(rd) s it stops due to retrding torque τ If the torque is doubled, nd the initil ngulr speed is hlved, through bout wht ngle does it rotte s it stops? () ϑ/16 (b) ϑ/2 (c) ϑ/4 (d) ϑ/8 (e) ϑ 8-11) girl initilly running with constnt velocity v jups onto the outer edge of erry-go-round s shown t the right, nd therefter rottes with the erry-go-round To solve for the ngulr velocity of the erry-go-round plus girl, which of the following lws should be used? () conservtion of ngulr oentu only (b) conservtion of liner oentu only (c) conservtion of kinetic energy only (d) conservtion of ngulr oentu nd kinetic energy (e) conservtion of liner oentu nd kinetic energy v Merry-go round

2 Phy 231 Sp 3 Hoework #8 Pge 2 of ) piece of cly of ss = 2 kg is initilly sliding on horizontl frictionless tble top with constnt speed v = 6 /s towrd the iddle of unifor rod of length = 1 nd ss M = 3 kg tht is pivoted bout one end (point ) nd is initilly t rest The cly sticks to the rod where it hits bout wht is the resulting ngulr velocity ω of the rod plus cly? I(rod) = (1/3)M 2 () 1 rd/s (b) 6 rd/s (c) 2 rd/s (d) 4 rd/s (e) 3 rd/s v 8-13) student is holding two equl dubbells t rs length nd is stnding on circulr tble tht is rotting without friction with constnt ngulr speed ω If, without oving nything else, the student siply drops the dubbells, which one of the following stteents is WRONG? Neglect ir resistnce, nd consider the proble ieditely fter the dubbells re relesed () The ngulr oentu of ech dubbell is conserved (b) The student continues to rotte with ω (c) The dubells initilly ove rdilly outwrd (d) The student's ngulr oentu is conserved (e) The student's kinetic energy is conserved 8-14) Which one of the following stteents is WRONG? () or clculting the oent of inerti, the ss of body cnnot siply be considered s concentrted t its center of ss (b) If unifor cylinder nd hoop, hving the se outer rdius nd the se totl ss, roll side by side down n inclined plne, both strting fro rest, then the cylinder should rech the botto of the plne first (c) If girl sitting on horse on erry -go-round throws bll rdilly outwrd, then the ngulr oentu of the girl plus erry-go- -round stys constnt (d) If prticle oves in stright line with constnt velocity, its ngulr oentu bout ny fixed point stys constnt s it oves (e) solid cylinder rolls without slipping down two different inclined plnes of the se height but different ngles of inclintion Its speed t the botto is fster for the plne with the lrger ngle of inclintion 8-15) Which one of the following stteents is WRONG? ( ) cockroch is initilly t rest on the perieter of sttic turntble tht hs n lost frictionless bering but rough top surfce If the cockroch now wlks clockwise round the perieter, the turntble should rotte counterclockwise (b) Ruth nd Roger re cycling together t the se liner speed The wheels of Ruth's bike hve little lrger dieter thn those of Roger's The ngulr speed of Ruth's wheels is little slower thn the ngulr speed of Roger's wheels (c) If cr's speedoeter reds speed proportionl to the rottion speed of its rer wheels, then one ust correct the reding when using tires of different dieter (eg, snow tires) (d) If globl wring elted the ice cps, nd the resulting wter ws dis tributed closer to the equtor, the length of the dy on rth should decrese (e) high diver rotting in the lyout position (lrge oent of inerti bout her center of grvity) cn rotte fster by drwing her legs up ginst her chest ( tuck position = sller oent of inerti bout her center of grvity) 8-16) deonstrtor is rotting t constnt ω on chir with frictionless berings She initilly hs her rs out, holding weights so tht her totl oent of inert i is I When she brings the weights in to her chest, her oent of inerti decreses to I/2 Wht is the rtio of her finl kinetic energy to her initil kinetic energy? () 1 (b) 2 (c) ½ (d) ¼ (e) ) Which one of the following stteents is WRONG? () The oent of inerti of body will generlly chnge s the xis of rottion is chnged (b) The oent of inerti of thin rod is lrger bout its end thn bout its center (c) The oent of inerti of unifor cylinder of given ss nd rdius is sller thn tht of hoop of the se ss nd rdius (d) The center of grvity of body cn be outside the physicl prt of the body (ie, it cn be in epty spce) (e) If the center of grvity of body is t rest, then no prt of the body cn be oving in ny wy 8-18) wheel of rdius r = 2 rolls without slipping on flt ground If the liner speed of its center of ss is 6 /sec reltive to the ground, wht is its ngulr speed of rottion ω bout its center of ss? () 12 rd/s (b) 3 rd/s (c) 6π rd/s (d) 24π rd/s (e) 12π rd/s 8-19) disk of ss, rdius R, nd oent of inerti I, strts fro rest nd rolls without slipping down hill of height h Its liner kinetic energy t the botto of the hill is: () gh (b) gh(1 + I/R 2 ) (c) gh/(1 + I/R 2 ) (d) gh/(i/r 2 ) (e) None of these is correct

3 Phy 231 Sp 3 Hoework #8 Pge 3 of 4 8-1) rigid squre object of negligible weight is cted upon by the forces 1 nd 2 shown t the right, which pull on its corners The forces re drwn to scle in ters of the dotted lines Which one of the lbelled forces nd loctions will produce equilibriu? () (b) (c) (d) (e) 8-2) force = 1 N is pulling on one end of stick of length = 4 bout wht re the gnitudes of the torques (in N-) bout the other end of the stick (point ) when the force is pplied in the three different cses,,, nd shown t the right () = 4, =, = 2 (b) =, = 4, = 2 (c) = 4, =, = 35 (d) = 35, =, = 4 (e) = 2, = 35, = o unifor rod of ss 9 kg nd length = 2 is ttched to wll t one end by pivot nd t the other end by horizontl string The rod is in sttic equilibriu t n ngle of 53 o with the wll Wll String T 8-3) bout wht is the gnitude of the horizontl force h on the rod t the pivot? () 8 N (b) 23 N (c) 3 N (d) 6 N (e) 4 N 8-4) bout wht is the gnitude of the verticl force v on the rod t the pivot? () 9 N (b) 45 N (c) 3 N (d) 72 N (e) 54 N 8-5) The center of grvity of the thick wire object shown t the right is closest to point: () (b) (c) (d) (e) v 53 o h 8-6) Two strong children on ice sktes, one of ss 1 = 2 kg nd one of ss 2 = 6 kg, re holding the ends of unifor rod of ss 2 kg nd length 2 s shown t the right The children grdully pull theselves together to the iddle of the rod If you cn neglect friction with the ice, bout how fr should they be fro the strting position of the sller (2 kg) child, when they rech the iddle of the rod? () 14 (b) 1 (c) 11 (d) 18 (e) You don't hve enough infortion to tell ) One unifor solid cylinder of wood hs ss M, length nd rdius R second unifor solid cylinder de of the se wood lso hs ss M, but hs length 2 nd whtever rdius r is need to ke the totl ss sty equl to M The oent of inerti of the second cylinder (round its cylindricl xis) copred to the first one is: () lrger (b) sller (c) the se (d) you need to know the rdii to tell (e) you need to know both the sses nd the rdii to tell 8-8) Wht is the oent of inerti bout the xis (sticking out of the pge) of the four equl sses shown t the right? () 4 2 (b) 1 2 (c) 6 2 (d) 8 2 (e) ) cylinder with n initil ngulr speed ω 1 = 2 rd/s bout its center of ss is stopped by torque τ = -1 N The totl tie it tkes to stop is t 1 = 2 s How long would it tke the se cylinder to stop if it is cted upon by the se torque, but strts with n initil ngulr speed ω 2 = 4 rd/s? () 4π s (b) 8π s (c) 4 s (d) 1 s (e) 2 s 8-1) disk of rottionl inerti I, initilly rotting with ngulr speed ω, oves through n ngle ϑ(rd) s it stops due to retrding torque τ If the torque nd the initil ngulr speed re both doubled, through bout wht ngle does it rotte s it stops? () ϑ/8 (b) ϑ/4 (c) ϑ/2 (d) ϑ (e) 2ϑ 8-11) person is rotting on frictionless bse with her rs extended outwrd holding two 1 kg weights When she pulls her rs stright in, which one of the following stteents is ORRT? () Her ngulr oentu nd kinetic energy both increse (b) Her ngulr oentu is constnt, but her kinetic energy increses (c) Her ngulr oentu nd kinetic energy re both constnt (d) Her ngulr oentu nd kinetic energy both decrese (e) Her ngulr oentu is constnt, but her kinetic energy decreses 2 2

4 Phy 231 Sp 3 Hoework #8 Pge 4 of ) piece of cly of ss = 2 kg is initilly sliding on horizontl frictionless tble top with constnt speed v = 6 /s towrd the end of unifor rod of length = 1 nd ss M = 3 kg tht is pivoted bout one end (point ) nd is initilly t rest The cly sticks to the rod where it hits bout wht is the resulting ngulr velocity ω of the rod plus cly? I(rod) = (1/3)M 2 () 1 rd/s (b) 6 rd/s (c) 2 rd/s (d) 4 rd/s (e) 3 rd/s v 8-13) student is holding two equl dubbells t rs length nd is stnding on circulr tble tht is rotting without friction with constnt ngulr speed ω If, without oving nything else, the student siply drops the dubbells, which one of the following stteents is WRONG? Neglect ir resistnce, nd consider the proble ieditely fter the dubbells re relesed () The ngulr oentu of ech dubbell is conserved (b) The student strts to rotte with ngulr speed fster thn ω (c) The dubells initilly ove tngentilly (d) The student's ngulr oentu is conserved (e) The student's kinetic energy is conserved 8-14) Which one of the following stteents is WRONG? () or clculting the oent of inerti, the ss of body cnnot siply be considered s concentrted t its center of ss (b) If unifor cylinder nd hoop, hving the se outer rdius nd the se totl ss, roll side by side down n inclined plne, both strting fro rest, then the hoop should rech the botto of the plne first (c) If girl sitting on horse on erry -go-round throws bll rdilly outwrd, then the ngulr oentu of the girl plus erry-go- -round stys constnt (d) If prticle oves in stright line with constnt velocity, its ngulr oentu bout ny fixed point stys constnt s it oves (e) solid cylinder rolls without slipping down two different inclined plnes of the se height but different ngles of inclintion Its speed t the botto is the se for both plnes 8-15) Which one of the following stteents is WRONG? ( ) cockroch is initilly t rest on the perieter of sttic turntble tht hs n lost frictionless bering but rough top surfce If the cockroch now wlks clockwise round the perieter, the turntble should lso rotte clockwise (b) Ruth nd Roger re cycling together t the se liner speed The wheels of Ruth's bike hve little lrger dieter thn those of Roger's The ngulr speed of Ruth's wheels is little slower thn the ngulr speed of Roger's wheels (c) If cr's speedoeter reds speed proportionl to the rottion speed of its rer wheels, then one ust correct the reding when using tires of different dieter (eg, snow tires) (d) If globl wring elted the ice cps, nd the resulting wter ws distributed closer to the equtor, the length of the dy on rth should increse (e) high diver rotting in the lyout position (lrge oent of inerti bout her center of grvity) cn rotte fster by drwing her legs up ginst her chest ( tuck position = sller oent of inerti bout her center of grvity) 8-16) deonstrtor is rotting t constnt ω on chir with frictionless berings He initilly hs his rs in, holding weights so tht his totl oent of inerti is I When he extends his rs outwrd, his oent of inerti increses to 3I bout wht is the rtio of his finl kinetic energy to his initil kinetic energy? () 1 (b) 1/3 (c) 1/9 (d) 3 (e) ) Which one of the following stteents is WRONG? () The oent of inerti of body will generlly chnge s the xis of rottion is chnged (b) The oent of inerti of thin rod is lrger bout its end thn bout its center (c) The oent of inerti of unifor cylinder of given ss nd rdius is sller thn tht of hoop of the se ss nd rdius (d) The center of grvity of body cnnot be outside the physicl prt of the body (ie, it cn t be in epty spce) (e) If the center of grvity of body is t rest, the body cn still be rotting bout its center of grvity 8-18) wheel of rdius r = 2 is rolling without slipping on flt ground If the wheel's ngulr speed of rottion bout its center of ss is ω = 4 rd/sec, wht is the liner speed of its center of ss? () 2π /s (b) 16π /s (c) 2 /s (d) 4π /s (e) 8 /s 8-19) disk of ss, rdius R, nd oent of inerti I, strts fro rest nd rolls without slipping down hill of height h Its rottionl kinetic energy t the botto of the hill is: () gh (b) gh/(1 + I/R 2 ) (c) gh/(1 + R 2 /I) (d) gh(1 + R 2 /I ) (e) None of these is correct

5 8-1) b 2) d 3) e 4) 5) c 6) c 7) b 8) 9) 1) d 11) 12) d 13) c 14) e 15) d 16) b 17) e 18) b 19) c 8-1) e 2) c 3) d 4) 5) d 6) 7) b 8) e 9) c 1) e 11) b 12) d 13) b 14) b 15) 16) b 17) d 18) e 19) c