Announcements. Description Linear Angular position x θ displacement x θ rate of change of position v x ω x = = θ average rate of change of position

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Kristina Watts
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1 Announcement In the lectue link Look o tet 1 beakdown liting the topic o the quetion. Look o m umma o topic o the eam. We ll ue it on the eiew net Tueda. Look o a lit o baic phic act eleant o thi eam. Eta poblem oling eion Sunda June 10 at 7 PM in NPB 100. Tet will be on ection 1.1 though 5.6. Toda we inih Chapte 5. Chapte 5 Cicula Motion The language ued to decibe otational motion i e imila to the language ued to decibe linea motion. The mbol ae dieent. Deciption Linea Angula poition θ diplacement θ ate o change o poition ω, a ω a θ aeage ate o change o poition θ lim ω lim intantaneou ate o change o poition t 0 t 0 While we ae amilia with angle meaued in degee, we meaue otation in adian. In the igue, the angle meaue in adian i deined a the atio o the ac length to the adiu : θ Fo a complete otation, π and the angle o a complete otation i π adian. Thi gie the coneion o adian to degee o 360 π ad

Thee i a elation between the peed o a point on the im and the angula elocit o the wheel.

We take counteclockwie otation a poitie and clockwie otation a negatie.

The equenc () The numbe o eolution pe unit time. Thee paamete ae elated.

2 Thee i a elation between the peed o a point on the im and the angula elocit o the wheel. θ θ θ ω Jut like diplacement, otation hae diection. We take counteclockwie otation a poitie and clockwie otation a negatie. Othe ueul paamete The peiod (T) The time it take o a compete eolution. The equenc () The numbe o eolution pe unit time. Thee paamete ae elated. B deinition 1 T A complete eolution i the cicumeence π. The peed i the ditance diided b the time. Fo a complete eolution, the time i the peiod T π T π Uing the equation nea the top o the page, we hae ω π ω π Rolling motion I the wheel oll aco the gound, it peed depend on how at it pin.

3 I the wheel oll without lipping, the ale o the wheel moe with a peed o gien b Thi i a elatie elocit poblem! ω Radial Acceleation A paticle undegoing uniom cicula motion (ω i contant in time), till acceleate een though it peed i contant. The elocit continuoul change diection. The change in elocit point towad the cente o the cicle. The magnitude o the adial acceleation i A deiation i gien on page a Poblem-Soling Stateg o an Object in Uniom Cicula Motion (page 155) 1. Begin a o an Newton econd law poblem: identi all the oce acting on the object and daw an FBD.. Chooe pependicula ae at the point o inteet o that one i adial and the othe i tangent to the cicula path. 3. Find the adial component o each oce. 4. Appl Newton econd law a ollow: F ma whee ΣF i the adial component o the net oce and the adial acceleation i a ω

(Fo uniom cicula motion, neithe the net oce no the acceleation ha a tangential component.) Banked and Unbanked cue A ca tuning though a cue at contant i acceleated towad the cente o the cue.

Fom the diagam aboe (note the diection o -ai i conta to ou conention) F ma m F ma N mg 0 What i the atet ae peed o a cue? That i when the ca need the laget poible tatic ictional oce in the cue.

4 (Fo uniom cicula motion, neithe the net oce no the acceleation ha a tangential component.) Banked and Unbanked cue A ca tuning though a cue at contant i acceleated towad the cente o the cue. I the oad i lat, the adial oce i upplied b iction. I the ca i olling, the adial oce i tatic iction. I it i liding, it i kinetic iction. Fom the diagam aboe (note the diection o -ai i conta to ou conention) F ma m F ma N mg 0 What i the atet ae peed o a cue? That i when the ca need the laget poible tatic ictional oce in the cue. m,ma ma µ N µ mg µ g The maimum ae peed depend on the coeicient o iction. The lowe µ, the lowe the ca mut go. (Slow down on wet teet!) the adiu o the cue. Go low aound hap cue (whee i mall)! the acceleation due to gait. (Be caeul diing on the moon!!!) The ituation can be impoed b banking the cue.

The needed adial oce in upplied b a component o the nomal oce. Impotant to notice that the -ai doe not point down the incline. It point in the diection o the adial acceleation to the let.

5 The needed adial oce in upplied b a component o the nomal oce. Impotant to notice that the -ai doe not point down the incline. It point in the diection o the adial acceleation to the let. The ca doe not lide down the incline. It i acceleated towad the cente o the cue. F ma N m N in θ m N F ma W 0 N coθ mg Diiding the two equation to eliminate the nomal oce m N inθ N coθ mg tanθ g A ca taeling thi peed aound a cue banked at angle θ with adiu, will not equie an iction to ael tael aound the cue. What happen i the ca goe too at? What happen i the ca goe too low?

6 Cicula obit The Eath emain in obit aound the un becaue o the gaitational pull o the un. Gaitation upplie the adial oce needed to keep the Eath in it obit. The ame phic occu with atellite in obit aound the Eath. Ate woking o 0 ea with the obeation o Tcho Bahe, Johanne Keple tated hi thee law o planeta motion: The planet tael in elliptical obit with the Sun at one ocu o the ellipe. A line dawn om a planet to the Sun weep out equal aea in equal time inteal. The quae o the obital peiod i popotional to the cube o the aeage ditance om the planet to the Sun. In a emakable eiication o hi law o gaitation, Newton wa able to deie Keple law. Nonuniom Cicula Motion Suppoe the otating wheel change it angula peed. Thee i now a tangential acceleation a well a the adial acceleation we hae tudied. Since the adial and tangential diection ae pependicula to each othe, the oeall acceleation i a a + a t Poblem-Soling Stateg o an Object in Nonuniom Cicula Motion (page 165) 1. Begin a o an Newton econd law poblem: Identi all the oce acting on the object and daw an FBD.. Chooe pependicula ae at the point o inteet o that one ai i adial and the othe i tangent to the cicula path. 3. Find the adial component o each oce. 4. Appl Newton econd law along the adial diection:

7 F ma whee a ω 5. I necea, appl Newton econd law to the tangential oce component: F t ma t The tangential acceleation component at detemine how the peed o the object change. Poblem 5.41 A ca appoache the top o a hill that i haped like a etical cicle with a adiu o 55.0 m. What i the atet peed that the ca can go oe the hill without loing contact with the gound? Tangential and Angula Acceleation We can add ow to ou table Deciption Linea Angula poition θ diplacement θ Rate o change o poition ω, a ω a θ Aeage ate o change o poition lim ω θ lim Intantaneou ate o change o poition Aeage ate o change o peed Intantaneou ate o change o peed The component o acceleation ae a a, a t 0 lim t 0 ω a t α a t 0 α ω a ω α lim t 0 Uing imila eaoning to what we ued o uniom linea motion, we can ceate equation o uniom angula motion.

8 Uniom Linea Motion Uniom Angula Motion a contant α contant a ω ω ω α i ( + ) t i θ ( ω + ωi ) i 1 ) a ( a i θ ω + i i 1 ) α( ω ω α θ Poblem 4.5 A dik otate with contant angula acceleation. The initial peed o the dik i π ad/. Ate the dik otate though 10π adian, the angula peed i 7π ad/. (a) What i the magnitude o the angula acceleation? (b) How much time did it take o the dik to otate though 10π adian? (c) What i the tangential acceleation o a point located at a ditance o 5.0 cm om the cente o the dik? i

SPH3UW/SPH4U Unit 3.2 Forces in Cetripetal Motion Page 1 of 6. Notes Physics Tool Box

SPH3UW/SPH4U Unit 3.2 Forces in Cetripetal Motion Page 1 of 6. Notes Physics Tool Box SPH3UW/SPH4U Unit 3. Foce in Cetipetal Motion Page 1 o 6 Note Phyic Tool Box Net Foce: acting on an object in uniom cicula motion act towad the cente o the cicle. Magnitude o Net Foce: combine Newton Second