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This 4 page Class Notes was uploaded by Willard Grady on Monday October 5, 2015. The Class Notes belongs to PHY110 at Central Michigan University taught by Staff in Fall. Since its upload, it has received 13 views. For similar materials see /class/218951/phy110-central-michigan-university in Physics 2 at Central Michigan University.
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Date Created: 10/05/15
VI ANGULAR MOTION A About Angular Motion 1 ery important type ofmotion in a moving in a circular path Circular motion is very common Give some examples Orbiting planets gears in a machine CD s b An important case is rotation spin i We have seen how one can study the overall motion of a body path of a baseball speed ofa falling object how a moving object is slowed by friction etc ii A body s spin is also important May affect the body s motion curve balls Can be complicated 3 spins a once iii Note that spin is circular motion each part ofa spinning body moves in a circle 2 We measure rotational motion by the angle tumed Angle e a Look at a rotating wheel b In a certain time it rotates through an an le 9 c We can measure the angle or the angular distance by De example 36 Revolutions example 11039h rev 01 rev Note 1 rev 360 is d There is a third way to measure angles Degree units are arbitrary no good reason for it hy was this unit chosen 7 An angle unit that is not arbitrary is the radian 3 Radian measure a Again look at the wheel b An angle 0 corresponds to a distance on the rim s c The size ofs depends on Angle 0 and radius r d We can measure the angler as a ratio of s to r s e 7 0 is In radians r 4 Relatlonslups lrev 36W 27v rad Examplel What 15 a 90 angle expressedm radlans andrevolutlons7 690 27t360 m2 rad Examgle 2 What ls one radlan expressedln olegrees anolreyolutaons7 elraol 3oo 2ttraol lraol lrey2ttraol 0 lsrev B Angular yeloerty m l 20 rpm rneans twenty reyolutrons per rnrnute Thls ls an angle per tune unrt or an angularyeloerty We eontrnue to use Greek letters for angular rnotron e 7 angle 0 r angularveloclty 2 lee forllnearmouon we de ne angularyeloerty as a Y teehnreally ayeetor How7 a one agam we rnustrernernberthe dlfference between 7 average angular yeloerty m r rnstantaneous angularyeloerty m b The best unrt for angularyeloerty ls radsee many others are posslble c Angular aeeelerauon u How fastthe angular yeloerty ls ehangrn ls ealleol angular aeeelerauon u 2 Llnear aeeeleratronrs a V1 7 V t Angular aeeelerauon ls u we r on t 3 An example When abowllng ball ls rstreleaseolrt slldes olown the alley before rt starts rolllng Iflttakes l 2 seeonols for abowllng ball to attan an angular yeloerty of reysee oleterrnrne the average angular aeeeleratron ofthe bowllng ball tuft o yseer 392 see 2 11 77 i5r2vse z l2see see Note unrts of angular aeeeleratron are angular yeloerty dlvlded by tune quot ve 2 quotgt a Best unrtrs radsee D Angular Mouon anol Constant Angular Aeeelerauon 1 one has the same types ofequauons as for lrnearrnouon An ouon d le Velocl V olt A ularyeloerty 0 ext Aeeelerauon avrrvrt Angular u my 7 nont ng ng The four basic equations VrViat mrmidt d 2VrVit 9 2ul otit dVit 2at2 e wlt 20tz vp1v22ad mp2m2a9 3 Exarnple A skater initially turning at 3 revsec slows down with constant angular deceleration and stops in 4 seconds Find her angular deceleration and the number ofrevolutions she makes before stopping Know ml 0revsec t 4 sec Calculate it use equation 1 o 075 revsec2 why the minus Sign Now find total revolutions covered sing equ ion e 3 revsec 4 sec lax075 revsec24 sec2 12 rev 6rev e 6rev before stopping n rotational and linear motion are connected Connection between Rotational and Translational Motion 1 Ofte 2 For example there is obviously a connection between how fast awheel rotates and how far it travels ll lt s gt a Look at the reference point on the rim Distance wheel travels is s The rotational distance is also s and s re b Now consider the speed ofthe wheel u r t Linearspeed v st gt v ret c Similarly a rot 3 Important notes a These equations work only ifwe use radian rneasure b 9ma arethesamefor pointsofarigidbody u n u u u t unit c s V a an p r center ofrotation father out the faster the speed Centripetal Force 1 From Newton s 1St Law a body will not change speed or direction unless acted upon by a force Therefore a force is required for circular motion It is called the centripetal force a Centripetal force in the generic name b An example a car going around a comer Centripetal force is needed to change the car s direction This force is provided by the friction force between the tires and the road c Other examples of centripetal forces Tension in a string keeping a ball moving in a circle Gravity keeping the earth orbiting about the sun The amount of centripetal force needed to keep a body moving in a circle depends on a the mass of the object b The speed of the object the speed is moving c The radius of the circle mV2 Centripetal Force FCEN From F ma centripetal acceleration is aCEN 7 r Exam les Example 1 A 1200 kg 2640 lb car is turning a corner at a speed of8 msec 18 mph and it travels along the arc of a circle in the process If the radius of this circle is 9 In what is the centripetal force required to hold the car in the circular path FCEN 1200 kg8 msec 8533 N 9 meters This amount of force is needed to turn a 9 m 30 ft radius curve If we look at the friction equation F u R where R is the weight W mg we see u 8533 120010 071 What about at 2 m sec faster 22 mph What about a wet or icy road k 11 impossible Example 2 The old water trick How fast do I have to swing the pail Centripetal acceleration must be greater than accel of gravity r gt g r 1meter g 10msec2 V rm 1 xm2l gt 10 m gt 316 radsec 05 revsec 30 rpm
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