Rotational Kinetic Energy

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Clifton Pearson
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1 Add Impotant Rotational Kinetic Enegy Page: 353 NGSS Standad: N/A Rotational Kinetic Enegy MA Cuiculum Famewok (006):.1,.,.3 AP Phyic 1 Leaning Objective: N/A, but olling poblem have appeaed on peviou AP exam. Knowledge/Undetanding Goal: Skill: what otational kinetic enegy i diffeence between otational and tanlational kinetic enegy calculate the otational kinetic enegy of an object olve conevation of enegy poblem involving object that have linea motion (tanlational kinetic enegy) and ae alo otating (otational kinetic enegy) Language Objective: Undetand and coectly ue the tem otational kinetic enegy. Set up and olve wod poblem involving otational kinetic enegy and conevation of enegy with otating object. Lab, Activitie & Demontation: Note: Calculate the exact landing pot of golf ball olling down a amp. Jut a an object that i moving in a taight line ha kinetic enegy, a otating object alo ha kinetic enegy.

Add Impotant Rotational Kinetic Enegy Page: 354 When the log in the above pictue i otating, it tanfe ome of it kinetic enegy to the people tying to tand on it, thowing one of them into the wate.

2 Add Impotant Rotational Kinetic Enegy Page: 354 When the log in the above pictue i otating, it tanfe ome of it kinetic enegy to the people tying to tand on it, thowing one of them into the wate. In a otating ytem, the fomula fo kinetic enegy look imila to the equation fo kinetic enegy in linea ytem, with ma (tanlational inetia) eplaced by moment of inetia (otational inetia), and linea (tanlational) velocity eplaced by angula velocity: K 1 t mv K 1 I tanlational otational

3 Add Impotant Rotational Kinetic Enegy Page: 355 Sample Poblem Q: What i the otational kinetic enegy of a tenpin bowling ball that ha a ma of 7.5 kg and a adiu of 10.9 cm a it oll down a bowling lane at 8.0? A: The otational kinetic enegy i: K 1 I We can find the angula velocity fom the tanlational velocity: v 8.0 (0.109) ad The bowling ball i a olid phee. The moment of inetia of a olid phee i: I I 5 5 (7.5)(0.109) I kgm To find the otational kinetic enegy, we plug thee numbe into the equation: K K K 1 ( 1 m I J )(0.0345)(73.3) m

4 Add Impotant Rotational Kinetic Enegy Page: 356 Total Kinetic Enegy If an object (uch a a ball) i olling, then it i otating and alo moving (tanlationally). It total kinetic enegy mut theefoe be the um of it tanlational kinetic enegy and it otational kinetic enegy: Sample poblem: K t 1 1 mv I K K total total Q: A tandad Type (medium) tenni ball i hollow and ha a ma of 58 g and a diamete of 6.75 cm. If the tenni ball oll 5.0 m aco a floo in 1.5, how much total enegy doe the ball have? K A: The tanlational velocity of the tenni ball i: d v t m The tanlational kinetic enegy of the ball i theefoe: K t 1 mv ( 1)(0.058)(4) J The angula velocity of the tenni ball can be calculated fom: v 4 ( ) The moment of inetia of a hollow phee i: ad -5 3 ( 3)(0.058)( ) kg m I m The otational kinetic enegy i theefoe: K 5 1 I ( 1)( )(118.5) J Finally, the total kinetic enegy i the um of the tanlational and otational kinetic enegie: K K t K J

5 Add Impotant Rotational Kinetic Enegy Page: 357 Homewok Poblem 1. A olid ball with a ma of 100 g and a adiu of.54 cm oll with a otational velocity of 1.0 ad. a. What i it otational kinetic enegy? Anwe: b. What i it tanlational kinetic enegy? 5 J Anwe: J c. What i it total kinetic enegy? Anwe: J

6 Add Impotant Rotational Kinetic Enegy Page: 358. How much wok i needed to top a 5 cm diamete olid cylindical flywheel otating at RPM? The flywheel ha a ma of 000 kg. Anwe: Nm 3. An object i initially at et. When 50 N m of wok i done on the object, it otate though 0 evolution in 4.0. What i it moment of inetia? Anwe: 0.17kg m

7 Add Impotant Rotational Kinetic Enegy Page: How much wok i equied to low a 0 cm diamete olid ball that ha a ma of.0 kg fom 5.0 to 1.0 m? m Anwe: 33.6 J 5. A flat dic that ha a ma of 1.5 kg and a diamete of 10 cm oll down a 1 m long incline with an angle of 15. What i it linea peed at the bottom? Anwe: 1.86 m

8 Add Impotant Ecape Velocity Page: 360 NGSS Standad: N/A Ecape Velocity MA Cuiculum Famewok (006):.1,.,.3 AP Phyic 1 Leaning Objective: N/A Knowledge/Undetanding Goal: how fat a ocket o pace hip need to tavel to ecape Eath (o any othe planet ) gavity how ecape velocity elate to gavitational potential enegy, kinetic enegy, and Newton Law of Univeal Gavitation Language Objective: Undetand and coectly ue the tem ecape velocity. Set up and olve wod poblem involving ecape velocity. Note: Ecape Velocity If you want to end a ocket o pace hip to exploe the et of the ola ytem o beyond, the ocket need enough kinetic enegy to ecape fom the foce of Eath gavity. To explain the calculation, it i neceay to undetand that ou fomula fo gavitational potential enegy i actually a implification. Becaue the foce of gavity attact object to the cente of the Eath, the equation hould be: U g mgh mg( h ho) whee h o i the ditance to the cente of the Eath (adiu of the Eath), and h i the total ditance between the object and the cente of the Eath. Nomally, we calculate gavitational potential enegy baed on a diffeence in height between ome height above the gound (h) and the gound (h = 0). Howeve, when we conide the poblem of ecaping fom the gavity of the entie planet, we need to conide the potential enegy elative to the cente of the Eath, whee the total foce of gavity would be zeo.

9 Add Impotant Ecape Velocity Page: 361 To do thi, the ocket kinetic enegy ( 1 mv ) mut be geate than o equal to the Eath gavitational potential enegy (mgh). Thi mean can wite thi in tem of Newton Law of Univeal Gavitation: 1 Gm1m mv Fg h h d 1 mv F h. We Howeve, becaue we need to ecape the gavitational pull of the entie planet, we need to meaue h fom the cente of the Eath, not the uface. Thi mean that at the uface of the eath, h in the above equation i the ame a in Newton Law of Univeal Gavitation. Similaly, the ma of the pacehip i one of the mae (let chooe m ) in Newton Law of Univeal Gavitation. Thi give: Gm1m Gm1m Fg h Fg 1 Gm1m m v e 1 Gm1 v e v e Gm planet At the uface of the Eath, whee m kg and m, v e 4 m m planet 4. (Thi equal appoximately mile pe hou.) g 6

10 Add Impotant Ecape Velocity Page: 36 Sample Poblem: Q: When Apollo 11 went to the moon, the pace hip needed to achieve the Eath ecape velocity of 1100 to ecape Eath gavity. What velocity m did the pace hip need to achieve in ode to ecape the moon gavity and etun to Eath? (I.e., what i the ecape velocity on the uface of the moon?) A: v v v e e e Gm d ()( m moon moon )( )

11 Add Impotant Powe Page: 363 NGSS Standad: N/A Powe MA Cuiculum Famewok (006):.4 AP Phyic 1 Leaning Objective: N/A, but powe poblem have appeaed on the AP exam. Skill: calculate powe Language Objective: Undetand and coectly ue the tem powe. Accuately decibe and apply the concept decibed in thi ection uing appopiate academic language. Set up and olve wod poblem involving powe. Note: powe: a meaue of the ate at which enegy i applied o wok i done. Powe i calculated by dividing wok (o enegy) by time. W P t K t U t Powe i a cala quantity and i meaued in Watt (W). 1 W 1 J N kgm m Note that utility companie meaue enegy in kilowatt-hou. Thi i becaue W P, which mean enegy = W = Pt. t Becaue 1 kw = 1000 W and 1 h = 3600, thi mean 1 kwh = (1000 W)(3600 ) = J Fd d Becaue W Fd, thi mean P F Fv t t

12 Add Impotant Powe Page: 364 Powe in Rotational Sytem In a otational ytem, the fomula fo powe look imila to the equation fo powe in linea ytem, with foce eplaced by toque and linea velocity eplaced by angula velocity: P Fv P linea Solving Powe Poblem otational Many powe poblem equie you to calculate the amount of wok done o the change in enegy, which you hould ecall i: W F d if the foce i caued by linea diplacement W if the wok i poduced by a toque 1 t v o K m( v ) if the change in enegy wa caued by a change in 1 o velocity K I ( ) if the change in enegy wa caued by a change in angula velocity mg h if the change in enegy wa caued by a change in U g height Once you have the wok o enegy, you can plug it in fo eithe W, ue the appopiate pat of the fomula: Ek o U, W K P t t and olve fo the miing vaiable. U Fv t

13 Add Impotant Powe Page: 365 Sample Poblem Q: What i the powe output of an engine that pull with a foce of 500. N ove a ditance of 100. m in 5? A: W Fd (500)(100) J P W t W 5 Q: A 60. W incandecent light bulb i poweed by a geneato that i poweed by a falling 1.0 kg ma on a ope. Auming the geneato i 100% efficient (i.e., no enegy i lot when the geneato convet it motion to electicity), how fa mut the ma fall in ode to powe the bulb at full bightne fo 1.0 minute? A: Ug mg h P t t (1)(10) h h 3600 h 360 m 10 Note that 360 m i appoximately the height of the Empie State Building. Thi i why changing fom incandecent light bulb to moe efficient compact fluoecent o LED bulb can make a ignificant diffeence in enegy conumption!

14 Add Impotant Powe Page: 366 Homewok Poblem 1. A mall nowmobile ha a W (1 hp) engine. It take a foce of 300. N to move a led load of wood along a pond. How much time will it take to tow the wood aco the pond if the ditance i meaued to be 850 m? Anwe: 8.3. A winch, which i ated at 70 W, i ued to pull an all-teain vehicle (ATV) out of a mud bog fo a ditance of.3 m. If the aveage foce applied by the winch i N, how long will the job take? Anwe: What i you powe output if you have a ma of 65 kg and you climb a 5. m vetical ladde in 10.4? Anwe: 35 W

15 Add Impotant Powe Page: Jack and Jill went up the hill. (The hill wa 3m high.) Jack wa caying a 1 kg pail of wate. If Jack ha a ma of 75 kg and he made the tip in 45, how much powe did he apply? Anwe: W 5. Jill, who ha a ma of 55 kg, made the ame tip a Jack did in poblem #3, but he took 10 econd le. How much powe did he apply? Anwe: W 6. The maximum powe output of a paticula cane i 1 kw. What i the fatet time in which thi cane could lift a kg cate to a height of 6.0 m? Anwe: The maximum powe output of a paticula cane i P. What i the fatet time, t, in which thi cane could lift a cate with ma m to a height h? (You may ue you wok fom poblem #6 above to guide you algeba.) Anwe: mgh t P

16 Add Impotant Powe Page: A 30 cm diamete olid cylindical flywheel with a ma of 500 kg wa acceleated fom et to an angula velocity of RPM in 60. a. How much wok wa done on the flywheel? Anwe: Nm b. How much powe wa exeted? Anwe: W

Physics 1114: Unit 5 Hand-out Homework (Answers)

Physics 1114: Unit 5 Hand-out Homewok (Answes) Poblem set 1 1. The flywheel on an expeimental bus is otating at 420 RPM (evolutions pe minute). To find (a) the angula velocity in ad/s (adians/second),