Rotational Kinematics. Rigid Object about a Fixed Axis Western HS AP Physics 1

Transcription

1 Rotatonal Knematcs Rgd Object about a Fxed Axs Westen HS AP Physcs 1

2 Leanng Objectes

3 What we know Unfom Ccula Moton q s Centpetal Acceleaton : Centpetal Foce: Non-unfom a F c c m F F F t m ma t

4 What we know q s Angula elocty and acceleaton q t t s q Tangental elocty and acceleaton a

5 Do 10 (?) A student twls a 0.75 kg lead weght aound he head. The adus of the moton s 0.50 m. a) How many adans n 040 degees? b) At what angle wll the weght hae taeled 9.0 metes? c) At t=0, q=0 and the elocty s 1.5 m/s. What s the angula elocty? d) What angula acceleaton wll ge a tangental acceleaton of 9.8 m/s/s? e) What angula elocty wll ge a centpetal foce of 95.0N? a) 35.6 adans b) 1031degees, 18 adans c) 3 ad/sec d) 19.6 ad/sec e) 15.9 ad/sec

6 Constant Angula Acceleaton If angula acceleaton s constant, we can deelop angula equatons of moton just as we dd fo tanslatonal moton q s t t x x a t t at t x x t at f f f f ) ( Axs) (Fxed Rotatonal Tanslatonal f f f f q q q q

7 Do 11 A bowlng ball wth a mass of 5.0 kg olls down a amp. a) If the ball acceleates fom 0.5 ad/s to.5 ad/s n 3.0 sec, what s the angula acceleaton? b) What angle dd the ball oll though n ths tme? c) What would be the ball s fnal angula elocty f t olled though an angle of 1080 degees wth the same angula acceleaton? a) 0.67 ad/s/s b) 4.5 adans, 57 degees c) 5 ad/sec

8 Decton Angula Velocty and Acceleaton ae ectos Fo otatonal moton, you must specfy an axs of otaton Angula elocty ecto s paallel to the axs Decton detemned by ght hand ule Cul fnges of ght hand n the decton of otaton thumb ponts n decton of angula elocty

9 Rgd Object s Pont Patcle In tanslatonal moton an extended object can be model as f t wee a pont In otatonal moton, the moton can t be modeled as a patcle snce eey pont has dffeent eloctes and acceleatons Must be modeled as a collecton of patcles A gd object can t be defomed the elate locaton of the patcles emans constant

10 Rgd Object Rotaton a a t c Each patcle that makes up the object has the same angula elocty and acceleaton Each patcle moes n a ccle about the axs of otaton Ccula moton equatons apply fo each patcle

11 Rotatonal Knetc Enegy Each patcle that makes up an object wll hae KE gen by: KE 1 m m 1 The total KE due to otaton then becomes: snce KE 1 m m 1

12 Example How many axes of otaton does ths object hae? +z =1.5m = =1.0m 3 How much otatonal KE does the object hae f t s otatng about the z-axs at.0 ad/s? KE KE KE 1 1 m m 1 (1) (1) 3(1.5) 3(1.5) 1 (17.5)(4) 35J

13 Do 1 A peson twls a 1.0 mete long baton n the a wth an angula elocty of.5 ad/sec aound ts cente of mass. The shaft has neglgble mass and one end has a mass of 0.5kg whle the othe end has a mass of 1.5kg. a) How fa fom the small end s the cente of mass? b) What s the otatonal knetc enegy of the baton? a) 0.71 m b) 1.1 J

14 Rotatonal Knetc Enegy KE 1 m m 1 The tem Sm occus n all otatonal moton poblems and s an object s Moment of Ineta, I I m Rotatonal Knetc Enegy KE 1 I

15 Rotatonal Ineta Ineta Is an object s esstance to a change n moton Moton can be lnea o otatonal Mass s a measue of an object s neta Rotatonal Ineta Is an object s esstance to a change n otatonal moton Rotatonal neta depends on whee the mass s located o an object s dstbuton of mass

16 Rotatonal Ineta The fathe an object s mass s located fom the axs, the geate ts otatonal neta An object s otatonal neta s measued by ts Moment of Ineta, I

17 Rotatonal Ineta Examples

18 On you own Poe that I fo a thn cylndcal shell about ts long axs (z) s MR.

19 Any Questons?