Add Imporan Angular Moion, Speed and Velociy Page: 163 Noe/Cue Here Angular Moion, Speed and Velociy NGSS Sandard: N/A MA Curriculum Framework (006): 1.1, 1. AP Phyic 1 Learning Objecive: 3.A.1.1, 3.A.1.3 Knowledge/Underanding Goal: underand erm relaing o angular poiion, peed & velociy Language Objecive: Underand and correcly ue he erm angle and angular velociy. Accuraely decribe and apply he concep decribed in hi ecion uing appropriae academic language. Lab, Aciviie & Demonraion: Noe: Swing an objec on a ring. If an objec i roaing (raveling in a circle), hen i poiion a any given ime can be decribed uing polar coördinae by i diance from he cener of he circle (r) and i angle (θ ) relaive o ome reference angle (which we will call 0 ). arc lengh (): he lengh of an arc; he diance raveled around par of a circle. r Ue hi pace for ummary and/or addiional noe. AP Phyic 1: Algebra-Baed
Add Imporan Angular Moion, Speed and Velociy Page: 164 Noe/Cue Here angular velociy (ω): he roaional velociy of an objec a i ravel around a circle, i.e., i change in angle per uni of ime. (For purpoe of comparion, he definiion of angular velociy i preened along wih i linear counerpar.) d x x xo v linear ω angular In general, phyici ue Greek leer for angular variable. The variable for angular velociy i he lower cae Greek leer omega (ω). Be careful o diinguih in your wriing beween he Greek leer ω and he Roman leer w. angenial velociy: he linear velociy of a poin on a rigid, roaing body. The erm angenial velociy i ued becaue he inananeou direcion of he velociy i angenial o he direcion of roaion. To find he angenial velociy of a poin on a roaing (rigid) body, he poin ravel an arc lengh of in ime. If angle θ i in radian, hen = rδθ. Thi mean: r vt rω and herefore vt rω Sample Problem: Q: Wha i he angular velociy ( rad ) in of a car engine ha i pinning a 400 rpm? A: 400 rpm mean 400 revoluion per minue. 400 rev 1min rad 4800 80 1min 60 1rev 60 rev rev 51 o Ue hi pace for ummary and/or addiional noe. AP Phyic 1: Algebra-Baed
Add Imporan Angular Moion, Speed and Velociy Page: 165 Noe/Cue Here Q: Find he oal diance raveled in 10 by a penny iing on a pinning dic wih a radiu of 0.5 m ha i roaing a a rae of 1 revoluion per. A: We are looking for he diance around he circle, which i he arc lengh. (Thi mean we need o work in radian.) r We know ha r = 0.5 m, bu we need o find ω. We know ha = 10, bu we need o find he angular velociy ω. rad 1 revoluion per i an angular velociy of ω. Now we can olve: ω ( )(10) 10 r (0.5)(10 ).5 m (.5)(3.14) 7.85m Exenion Ju a jerk i he rae of change of linear acceleraion, angular jerk i he rae of change of angular acceleraion. ζ α. (ζ i he Greek leer zea. Many college profeor canno draw i correcly and ju call i quiggle.) Angular jerk ha no been een on AP Phyic exam. Ue hi pace for ummary and/or addiional noe. AP Phyic 1: Algebra-Baed
Add Imporan Angular Moion, Speed and Velociy Page: 166 Noe/Cue Here Homework Problem 1. Through wha angle mu he wheel hown a he righ urn in order o unwind 40 cm of ring? Anwer: rad. Find he average angular velociy of a ofball picher arm (in rad ) if, in hrowing he ball, her arm roae one-hird of a revoluion on 0.1. Anwer: 0.9 rad 3. A golfer wing a nine iron (radiu = 1.1 m) wih an average angular velociy of 5.0 rad. Find he angenial velociy of he club head. Anwer: 5.5 m Ue hi pace for ummary and/or addiional noe. AP Phyic 1: Algebra-Baed
Add Imporan Angular Acceleraion Page: 167 Noe/Cue Here NGSS Sandard: N/A Angular Acceleraion MA Curriculum Framework (006): 1.1, 1. AP Phyic 1 Learning Objecive: 3.A.1.1, 3.A.1.3 Knowledge/Underanding Goal: Skill: wha angular acceleraion mean calculae angle, angular velociy and angular acceleraion for problem ha involve roaional moion. Language Objecive: Underand and correcly ue he erm angular acceleraion. Accuraely decribe and apply he concep decribed in hi ecion uing appropriae academic language. Lab, Aciviie & Demonraion: Noe: Swing an objec on a ring and hen change i angular velociy. If a roaing objec ar roaing faer or lower, hi mean i roaional velociy i changing. angular acceleraion (α): he change in angular velociy wih repec o ime. (Again, he definiion i preened wih he linear equaion for comparion.) v v a linear v o ω ω α angular A before, be careful o diinguih beween he lower cae Greek leer α and he lower cae Roman leer a. ω o Ue hi pace for ummary and/or addiional noe. AP Phyic 1: Algebra-Baed
Add Imporan Angular Acceleraion Page: 168 Noe/Cue Here A wih linear acceleraion, if he objec ha angular velociy and hen accelerae, he poiion equaion look like hi: x x o vo linear 1 a θ θ o ωo angular 1 α angenial acceleraion: he linear acceleraion of a poin on a rigid, roaing body. The erm angenial acceleraion i ued becaue he inananeou direcion of he acceleraion i angenial o he direcion of roaion. The angenial acceleraion of a poin on a rigid, roaing body i: a rα Sample Problem: T Q: A bicycli i riding a an iniial (linear) velociy of 7.5 m, and accelerae o a velociy of 10.0 over a duraion of 5.0. If he wheel on he bicycle have a m radiu of 0.343 m, wha i he angular acceleraion of he bicycle wheel? A: Fir we need o find he iniial and final angular velociie of he bike wheel. We can do hi from he angenial velociy, which equal he velociy of he bicycle. vo, T rωo 7.5 (0.343) ω ω o 7.5 0.343 o 1.87 Then we can ue he equaion: rad 7.8 5.0 1.46 rad vt rω 10.0 (0.343) ω ω ω ωo α 9.15 1.87 α(5.0) 7.8 5.0α α 10.0 0.343 9.15 rad Ue hi pace for ummary and/or addiional noe. AP Phyic 1: Algebra-Baed
Add Imporan Angular Acceleraion Page: 169 Noe/Cue Here An alernaive mehod i o olve he equaion by finding he linear acceleraion fir: v vo a 10.0 7.5 a(5).5 5a a.5 5 0.5 m Then we can ue he relaionhip beween angenial acceleraion and angular acceleraion: at rα 0.5 (0.343) α a α 1.46 rad 0.343 Homework Problem 1. A urnable roaing a 33⅓ RPM i hu off. I low down a a conan rae and coa o a op in 6. Wha i i angular acceleraion? rad Anwer: 0.135 Ue hi pace for ummary and/or addiional noe. AP Phyic 1: Algebra-Baed
Add Imporan Angular Acceleraion Page: 170 Noe/Cue Here. A urnable roaing wih an angular velociy of ω o i hu off. I low down a a conan rae and coa o a op in ime. Wha i i angular acceleraion, α? (You may ue your work from problem #1 above o guide you hrough he algebra.) Anwer: o 3. One of he demonraion we aw in cla wa winging a bucke of waer in a verical circle wihou pilling any of he waer. a. Explain why he waer ayed in he bucke. b. If he combined lengh of your arm and he bucke i 0.90 m, wha i he minimum angenial velociy ha he bucke mu have in order o no pill any waer? Anwer: 3.33 m Ue hi pace for ummary and/or addiional noe. AP Phyic 1: Algebra-Baed