Your Thoughts I get dizzy with ll the equtions being shifted, spun nd switched so much in the pre-lectures. If the pre-lectures for, 3 nd 4 re like tht, I m pretty worried. Are we going to be rcing spheres, Cylinders, nd hoops? I would like to put ll my money on the solid sphere if the msses nd rdius re the sme Just so I he better ide on wht is going on, for the collisions unit, did we just not ccount for rottion kinetic energy when we delt with two colliding blls? On the coming hour exm, do we ssume there is no rottionl kinetic energy? Clculus is so helpful for understnding physics...here's shout-out to clculus...thank YOU! My understnding of this topic nd my girlfriend he lot in common. They both dont exist. I got lost during the whole rottionl bit. Yeh, too bd tht ws the whole prelecture. Wht's blue nd smells like red pint? blue pint I don't know if it's just me, but these prelectures re getting progressiely hrder to follow long. This hs gien me nightmres since the AP test lst yer. Cries. Hey you! Yes, you! Do you like comedy, music, or mutnt Venus flytrps? If you nswered yes to ny of these questions, or if you he soul, you should come nd see Illini Student Musicl's production Little Shop of Horrors! Performing Mrch 8-30 t Lincoln Hll! Tickets ilble t illinistudentmusicls.org! You neer choose mine nywys...so blhblhblhblhblh! Mechnics Lecture 6, Slide
Might sound stupid becuse we he reched hlfwy through the semester but umm where do you uplod the homework question help thing, like the wlkthrough with the formuls? Did you know tht cts sleep for 70% of their life? Mechnics Lecture 6, Slide
nd Exm Wednesdy Mrch 7 th : 90 Minutes. Coers Lectures 7-3 only (No rottions on the exm) Regulr exm is t 7:00 pm Conflict exm is t 5:5 pm (sign up in grde-book) Double conflict t 3:00 pm (Bring officil proof of conflicts with other clsses t both 5:5 nd 7:00 to the stff in 33 Loomis) If you he triple conflict you need to contct Prof. Bezrydin (bezrydi@illinois.edu) Mechnics Lecture 9, Slide 3
Physics Lecture 6 Tody s Concepts: ) Rolling Kinetic Energy b) Angulr Accelertion Physics Lecture 6, Slide 4
Rolling Wht is ment by without slipping? If there is no slipping: R R Mechnics Lecture 6, Slide 5
Two wys of looking t rolling down rmp H PE M gh KE 0 Energy Consertion PE 0 KE K K trns rot Dynmics f Mg F m I Mechnics Lecture 6, Slide 6
Energy Consertion Objects of different I rolling down n inclined plne: K 0 U M g h h R M 0 0 K 0 K I U 0 M R K U 0 M gh I M Mechnics Lecture 6, Slide 7
Lets work out the generl cse K I K M c MR Use R nd I cmr. M c M Hoop: c Disk: c / Sphere: c /5 etc... So: c M Mgh gh c Doesn t depend on M or R, just on c (the shpe) Rmp demo Mechnics Lecture 6, Slide 8
Clicker Question A solid cylinder of mss M rolls long the floor without slipping with speed V. Wht is its totl kinetic energy? 3 A) K M V B) K M V C) K M V 4 Recll tht I cm M R for solid cylinder: Mechnics Lecture 6, Slide 9
I cm M R Mechnics Lecture 6, Slide 0
CheckPoint A block nd bll he the sme mss nd moe with the sme initil elocity cross floor nd then encounter identicl rmps. The block slides without friction nd the bll rolls without slipping. Which one mkes it furthest up the rmp? A) Block B) Bll C) Both rech the sme height. Mechnics Lecture 6, Slide
CheckPoint The block slides without friction nd the bll rolls without slipping. Which one mkes it furthest up the rmp? A) Block B) Bll C) Sme A) The block does not he kinetic energy wsted by rolling. B) The bll hs both trnsltionl KE (equl to tht of the block) nd rottionl KE. Becuse it hs more KE to strt with, it must he more PE to finish with, nd therefore it mkes it further up the rmp. C) since they he sme mss nd sme initil elocity, so they should rech the sme height of the rmp. Mechnics Lecture 6, Slide
CheckPoint A cylinder nd hoop he the sme mss nd rdius. They re relesed t the sme time nd roll down rmp without slipping. Which one reches the bottom first? A) Cylinder B) Hoop C) Both rech the bottom t the sme time Mechnics Lecture 6, Slide 3
Which one reches the bottom first? A) Cylinder B) Hoop C) Both rech the bottom t the sme time A) At the bottom both objects he combintion of kinetic trnsltionl nd rottionl motion, which re equl becuse they strted with the sme potentil energy. Since the hollow cylinder's moment of inerti is greter, its rottionl kinetic energy is greter, nd therefore the mount of energy tht becomes trnsltionl is less, mening it hs lower liner elocity thn tht of the solid cylinder. C) Since they both he the sme mss, nd strt t the sme height, they will he the sme potentil energy, nd will he the sme kinetic energy t the bottom. Mechnics Lecture 6, Slide 4
CheckPoint A smll light cylinder nd lrge hey cylinder re relesed t the sme time nd roll down rmp without slipping. Which one reches the bottom first? A) Smll cylinder B) Lrge cylinder C) Both rech the bottom t the sme time Mechnics Lecture 6, Slide 5
A) Smll cylinder B) Lrge cylinder C) Both rech the bottom t the sme time A) The smll cylinder hs less inerti thn the lrger cylinder. B) lrger cylinder hs more potentil energy to begin C) The mss nd rdius of ech cncel out when combining the moment of inerti nd kinetic energy equtions, which mens elocity only depends on the moment of inerti. Mechnics Lecture 6, Slide 6
Accelertion Mechnics Lecture 6, Slide 7
Accelertion Mechnics Lecture 6, Slide 8
Accelertion Accelertion depends only on the shpe, not on mss or rdius. Mechnics Lecture 6, Slide 9
Exmple Problem Suppose cylinder (rdius R, mss M) is used s pulley. Two msses (m > m ) re ttched to either end of string tht hngs oer the pulley, nd when the system is relesed it moes s shown. The string does not slip on the pulley. Wht is the ccelertion of the blocks? This wsn't too bd slide by slide, but I'd relly like to see "test style" questions bout this, nd wht pplictions we'll he to mke with wht we'e lerned. M R T T m m Mechnics Lecture 6, Slide 0
Clicker Question Suppose cylinder (rdius R, mss M) is used s pulley. Two msses (m > m ) re ttched to either end of string tht hngs oer the pulley, nd when the system is relesed it moes s shown. The string does not slip on the pulley. Compre the tension in the string on either side of the pulley: A) T > T B) T T C) T < T T M R T m m Mechnics Lecture 6, Slide
Atwood's Mchine with Mssie Pulley: A pir of msses re hung oer mssie disk-shped pulley s shown. Find the ccelertion of the blocks. For the hnging msses use F m m g - T m M R T - m g m T T m m m g m g Mechnics Lecture 6, Slide
Atwood's Mchine with Mssie Pulley: A pir of msses re hung oer mssie disk-shped pulley s shown. Find the ccelertion of the blocks. For the pulley use I I T R - T R (Since I I R MR R M R for disk) M R T T m m m g m g Mechnics Lecture 6, Slide 3
Atwood's Mchine with Mssie Pulley: We he three equtions nd three unknowns (T, T, ). Sole for. m g - T m () T - m g m () M R T - T M (3) T T m m m - m M g m m m g m g Mechnics Lecture 6, Slide 4
f M R We should go on bowling field trip to lern more bout rottionl dynmics I I fr I M gr MR 5 5 g R Mechnics Lecture 6, Slide 5
f M R F M F M Mg g M Mechnics Lecture 6, Slide 6
M R g 5 g R R 0 0 - t t t t 0 Once R it rolls without slipping 0 - t R R Rt t - t tr 0 5 g - gt t 0 7 g t 0 t 0 7 g Mechnics Lecture 6, Slide 7
M R x t - t 0 - t 0 Plug in nd t found in prts ) & 3) g t 7 g 0 Mechnics Lecture 6, Slide 8
M R Interesting side: how is relted to 0 : - t 0 0 - ( g ) 0 7 g - 0 0 7 t g 7 g 0 5 7 0 Doesn t depend on 0.74 0 We cn try this Mechnics Lecture 6, Slide 9