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# Introductory Physics I PHY 231

MSU

GPA 3.67

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This 15 page Class Notes was uploaded by Quinn Larkin on Saturday September 19, 2015. The Class Notes belongs to PHY 231 at Michigan State University taught by Staff in Fall. Since its upload, it has received 13 views. For similar materials see /class/207627/phy-231-michigan-state-university in Physics 2 at Michigan State University.

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Date Created: 09/19/15

Rotational Motion Angles Angular Velocity and Angular Acceleration Universal Law of Gravitation Kepler39s Laws ii Angular Displacement Circular motion about AXIS I Three differenl39 measures of angles 1 Degrees 2 Revolufions 1 rev 360 deg 3 Radions 2n rods 360 deg Aimgmbf EWmemgm a hmge Em d gm aee f mam T 0 P Reference line S 2 2W m mums remm ms a r isimm ams P 0 Reference line 2003 Thomson BrooksCole mile An automobile wheel has a radius of 42 cm If a car drives 10 km through what angle has the wheel rotated a In revolutions b In radians c In degrees Solution No re dis ronce cor39 moves dis ronce ou rside of wheel moves a Find N Known 3 10 000 m r 042 m Ni 3 789 2727 b Find 9 in radians Known N 9 27zradiansrevolutionN 9 238 x104 red C Find 9 in degrees Known N 9 360 degreesrevolution N 9 136 x106 deg E ngan 35 L Cm baa g wam m a Rc w w mg g a d mg g as UH a m AMng 9 a9quot a D f E mradmams a 7 L L mm pd ir W 6f 9 in remlu gns t O x 2 r 6f E6 in degees 2003 Thomson BrDDksICole 3 t 2 r 6f E 6 a 2 W 2 t 65 V 2 2 r ma Examlle A race car engine can turn at a maximum rate of 12 000 rpm revolutions per minute a What is the angular velocity in radians per second b If helipcopter blades were attached to the crankshaft while it turns with this angular velocity what is the maximum radius of a blade such that the speed of the blade tips stays below the speed of sound DATA The speed of sound is 343 ms Solution 3 Convert rpm to radians per second 12 0006 39 rad 1256 radianss sec rev 60 mm b Known v 343 ms 0 1256 rads Find r a Angular Acceleration I Denoted by 1 0f 0 t I a must be in radians per sec I Units of angular acceleration are rad2 I Every portion of The object has same angular Speed and same angular acceleration a Analogies Between Linear and Rotational Motion Rotational Motion Linear Motion Akmt ARM 2 2 A6 wtl at2 Axvitlat2 2 2 ozmioct vviat 2 0 2aA9 v2 vi22an Linear movement of a rotating point Distance I Different points on S 9quot the same object have I Speed different linear v or motions Acceleration a or Only works when 9 a and a are in radians A pottery wheel is accelerated uniformly from rest to a rate of 10 rpm in 30 seconds a What was the angular acceleration in rads2 bHow many revolutions did the wheel undergo during that time SolutiOI1 First find the final angular velocity in radianss wf1o ivj 1 2z j1047 j mm 60sec mm rev sec a Find angular acceleration mm 00349 rad2 t b Find number of revolutions Known 0350 of 1047 and t 30 First find A9 in radians f A6 7t rad A6rad 27zradrev 25 r39ev SolutiOI1 b Find number of revolutions Known 0350 0351047 and t 30 First find A9 in radians 0 A6 7ft 157 rad A6rad 27zradrev 25 r39ev

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