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by: Mrs. Peter Toy


Mrs. Peter Toy

GPA 3.96


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Class Notes
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This 13 page Class Notes was uploaded by Mrs. Peter Toy on Friday October 30, 2015. The Class Notes belongs to PHYS 2010 at University of Colorado at Boulder taught by Staff in Fall. Since its upload, it has received 33 views. For similar materials see /class/232106/phys-2010-university-of-colorado-at-boulder in Physics 2 at University of Colorado at Boulder.




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Date Created: 10/30/15
CTRot l A pocket watch and Big Ben are both keeping perfect time Which minute hand has the larger angular velocity on A Pocket watch s B Big Ben39s C Same n on both Which minute hand39s tip has the larger tangential velocity A Pocket watch s B Big Ben39s C Same 3 on DOCket both watch I Blg Ben Answers Both Big Ben and the pocket watch have the same magnitude angular velocity Big Ben has the larger tangential velocity v n r CTRot Z A small wheel and a large wheel are connected by a belt The small wheel is turned at a constant angular velocity 035 How does the magnitude of the angular velocity of the large wheel 03L compare to that of the small wheel S AnsoaL BnsgtoaL CnsltoaL DL There is a bug S on the rim of the small wheel and another bug L on the rim of the large wheel How do their speeds compare ASL BSgtL CSltL Answers 03s gt 03L Every time the big wheel turns once the little wheel turns several times So the small wheel turns thru more radians per sec S L Because the wheels are connected by a belt which does not slip when one bug moves an inch along the rim so does the other bug so they have the same speed CTRot 3 A ladybug is clinging to the rim of a spinning wheel which is spinning CCW and is speeding up At the moment shown when the bug is at the far right what is the approximate direction of the ladybug39s acceleration A BT C gt Dlt EV Answer The direction of the acceleration a is the same as the direction of AV The vlv2Av diagram looks like Av V2 V1 V2 V1 0 CTRot 4 A student in Physics 2010 sees the following question 1 on CAPA due the following Friday night An engine ywheel turns with constant angular speed of 100 revmin When the engine is shut off friction slows the wheel to rest in 2 hours What is the magnitude of the constant angular acceleration of the wheel Give the answer in units of revminz The student writes 03 0 az O 030 27 f 275100 revmin s0 locl t t 120 mln Does the answer come out correctly with the desired units of revmin2 A Yes B No Answer No You would write the exactly the same equations above if you were trying to get the answer in radminz The factor of 211 in the equation is actually 211 radrev so the units of the answer above are really radminz If you want the answer in revminz you have to leave out the factor of 211 or you can convert the answer in radmin2 to revmin2 by multiplying by the conversion factor 1 rev211 rad CTRot S Three forces labeled A B C are applied to a rod which pivots on an aXis thru its center cos45 sin45 1xE 0707 Which force causes the largest magnitude torque D two or more forces tie for largest size torque L I kc 4 2F L2 4 D I I 45 1 4 A B F L4 F Answer A For C i For B CTRot G A mass is hanging from the end of a horizontal bar which pivots about an axis through it center but it being held stationary The bar is released and begins to rotate As the bar rotates from horizontal to vertical the magnitude of the torque on the bar A increases B decreases C remains constant As the bar rotates from horizontal to vertical the magnitude of the angular acceleration 0c of the bar A increases B decreases C remains constant Answers The torque decreases ll F i decreases as the mass falls When the bar is vertical F i and the torque is zero As the bar rotates the angular acceleration decreases Here I the moment of inertia is constant The torque 139 decreases problem above so the angular acceleration or must decrease Although the angular velocity 03 is increasing in magnitude the angular acceleration is decreasing in magnitude CTRot 7 A light rod of length 2L has 2 small heavy masses each with mass m attached at the end and the middle The axis of rotation is at one end as shown What is the moment of inertia about the axis L L axis m m A2mL2 B4mL2 C5mL2 D8mL2 E None of these What is the magnitude of the net torque due to gravity A 2mgL B 3mgL C 4mgL D 5mgL If the bar is released from rest what is the magnitude of the initial angular acceleration A 3g5L B 5g3L C 7L3g D 3L5g Answers 1 5m L2 1 ZmIrIZ m1 r12 111er2 mL2 m2L2 mL24mL2 I Enet l 3mgL I In I 2 EI l ZZrIFii mgLmg2L both torques cause rotation in the same sense CW so the magnitudes of the torques add zlajah3mgL I 5mL2 0c 3g5L 139 net CTRot S A mallet consists of a heavy steel cubical head on a light wooden handle About which aXis of rotation is the moment of inertia I a maximum A I I I B C D Answer AXis B This aXis is farthest from the massive hammer head so for this aXis the moment of inertia will have the largest ri s CTRot 9 Two wheels each with the same radius R and the same total mass M are rotating about their xed axels Wheel A is a hoop with all the mass very near the rim Wheel B is a disk with the mass spread out uniformly Which has the larger momentofinertia I Zmi riz A Hoop B Disk C both have the same I hoop disk MR MR Answer The hoop has larger I The hoop has all its mass near the rim while the disk has its mass spread out between the aXis and the rim so larger r s for the same total mass results in a larger I CTRot 10 A mass m hangs from string wrapped around a pulley of radius R The pulley has a moment of inertia I and its pivot is frictionless Because of gravity the mass accelerates downward and the pulley rotates Which has greater magnitude the string tension FT or the weight mg A FT mg B FT lt mg C FT gt mg The magnitude of the torque on the pulley is A greater than ng B less than ng a C equal to ng Answers The string tension is less than mg and the magnitude of the torque is than ng The tension in the string is less than mg because the mass is accelerating down Considering the motion of the mass m we get The tension in the string FT is less than mg The torque is RFT which is less than ng CTRot ll A sphere a hoop and a cylinder all with the same mass M and same radius R are rolling along all with the same speed V Which has the most total kinetic energy lbostk A Sphere B Hoop C Disk D All have the same KE Sphere Answer Hoop KEm KEmms KErm 12M v2 12 I 032 All three have the same KEmmsl2M v2 The one with the largest KEm will have the greatest KEm That is the one with the largest I all have the same 03 vR IHOOIFMRZ IDiskl2MR2 Isphm25MR2 Hoop has the largest I You can see this intuitively the following way The hoop has all its mass at the rim where things move fastest speed at the top of the rim is 2v The others have mass near the middle where things move more slowly CTRot lZ Two hoops A and B both with the same mass M are each rotating about an aXis thru the center Hoop B has twice the diameter twice the R and is rotating at twice the rate twice the n as hoop A What is the ration KEB KEA A C R gt D D B C 2R 3 w m B4 C6 D8 E 16 Answer KE12Im2 LEE 303 1 KEA 5amp5 M2R22w2 2222 16 CTRot 13 A disk and a hoop both with the same mass M and the same radius R both start from rest and roll down an incline Which one has the largest total kinetic energy at the bottom A Disk B Hoop C same KEtm for both Answer Both have the same total KE Both start out with the same total PE mgh For both all of this initial PE is converted into KE Although they have the same total KE the disk has a larger translational KE and a small rotational KE so it is moving faster at the bottom CTRot 14 Consider a solid disk with an axis of rotation through the center perpendicular to the diagram The disk has mass M and radius R A small mass m is placed on the rim of the disk What is the moment of inertia of this system A MmR2 B less than MmR2 C greater than MmR2 Suppose that massdisk system is rotating and the axle is frictionless AtomAnt carries the mass m toward the center of the rotating disk As AtomAnt moves inward the magnitude of the angular momentum L of the system A increases B decreases C remains constant As AtomAnt moves inward the kinetic energy of the system A increases B decreases C remains constant Hint does AtomAnt do work Suppose the disk was on a phonograph player so that it always turned at 33 rpm As AtomAnt moves inward the speed of the mass m A increases B decreases C remains constant Answers 1 If the system is isolated from outside torques the total angmom L remains constant I decreases to increases but L 10 remains constant 2 KE increases Although L constant the ant does positive work in pushing the mass toward the center KEm 12 I 032 l2Ioaoa L 10 remains constant while 03 increases so KE increases 3 decreases Speed v 211 rT Constant rotation rate means constant period T As r gets smaller closer to axis v decreases Now we can see qualitatively why if the system is isolated the disk speeds up when the mass m moves toward the center If the tangential speed v decreases as the mass moves toward the center there must be a tangential not radial force on the mass causing it to slow down The disk is exerting a force tending to slow the mass m down By Newton39s third law there must be a equal and opposite force from the mass m on the disk tending to speed the disk up CTRot lS Two light massless rods labeled A and B each are connected to the ceiling by a frictionless pivot Rod A has length L and has a mass m at the end of the rod Rod B has length L 2 and has a mass 2m at its end Both rods are released from rest in a horizontal position A L2 L 2m m Which one experiences the larger torque A A B B C Both have the same size 5 Which one has the largest moment of inertia I about the pivot A A B B C Both have the same size I Which one falls to the vertical position fastest A A B B C Both fall at the same rate Hint a 1 1 Answers Both have the same size torque 1 A RFsinG ng sine 1 B RFsinG L22mg sine ng sine The one with the smallest I has the largest 0c since both have the same torque I A mLz IB 2mL22 12 mLz 13 has a smaller I a larger at so it falls faster CTRot 16 A star is rotating with a period T Over a period of a million years its radius decreases by a factor of 2 What is the new period of the star Hint Isphere M R2 AT2 B 2T C 4T C T4 E None ofthese Answer The new shorter period is T4 Angular momentum L I n 2 5MR2 211 T constant therefore RzT constant If R decreases by a factor of 2 then R2 decreases by a factor of 4 so T must decrease by a factor of 4 CTRot 17 Consider a solid disk with an aXis of rotation through the center perpendicular to the diagram The disk has mass M and radius R A small mass m is placed on the rim of the disk What is the moment of inertia of this system A MmR2 B less than MmR2 C greater than MmR2 Answer less than MmR2 1mm IDisk 1 12MR2 mR2 12M mR2 CTRot IS Consider two masses each of size 2m at the ends of a light rod of length L with the aXis of rotation through the center of the rod The rod is doubled in length and the masses are halved What happens to I A m L2 2m 2m A IAgtIB BIBgtIA C IAIB Answer IA lt 13 CTRot 19 Two wheels with xed axles each have the same mass M but wheel 2 has twice the radius of wheel 1 Each is accelerated from rest with a force applied as shown Assume that all the mass of the wheels is concentrated in the rims so that the moment of inertia of each is of the form I M R2 hoop formula In order to impart identical angular accelerations to both wheels how much larger is F than F1 Recall that E IOL F F1 2 Wheel 1 radius R mass M Wheel 2 radius 2R mass M AF2F1 BFz2F1 CFz4F1 DF28F1 E None ofthese Answer The moment of inertia I of the big hoop is 4 times bigger than the small hoop So for the big hoop we need a torque 4 times bigger to get the same angular acceleration Torque 139 r F i The larger hoop has a lever arm r twice as big as the small hoop so we need a force twice as big to get 4 times the torque CTRot ZO Consider a rod of uniform density with an aXis of rotation through its center and an identical rod with the aXis of rotation through one end Which has the larger moment of inertia C E aXis A IcgtIE BIcltIE CICIE Answer IE gt Ic If more of the mass is further from the aXis then the moment of inertia is bigger CTRot Zl A mass m is attached to a long massless rod The mass is close to one end ofthe rod Is it easier to balance the rod on end with the mass near the top or near the bottom Hint Small 0c means sluggish behaVior and 0c A easier with mass near top B easier with mass near bottom C No difference mg Answer the rod with the mass near the top is much easier to balance So as r increases the angular acceleration decreases Also think physically Big buildings take longer to fall over than do little pencils


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