Motion in a Plane Uniform Circular Motion
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1 Lectue 11 Chapte 8 Physics I Motion in a Plane Unifom Cicula Motion Couse website: PHYS.1410 Lectue 11 Danylo Depatment of Physics and Applied Physics
2 IN THIS CHAPTE, you will lean to sole poblems about motion in two dimensions. Today we ae going to discuss: Chapte 8: Unifom Cicula Motion: Section 8. Cicula Obits: Section 8.3 easoning about Cicula Motion: Section 8.4 PHYS.1410 Lectue 11 Danylo Depatment of Physics and Applied Physics
3 Let s ecall cicula motion An object is undegoing cicula motion Instantaneous elocity is tangent to the path Velocity is a ecto and has magnitude/diection) - tangential acceleation a t changes magnitude of the elocity, which is always tangent to the cicle. - centipetal acceleation a changes diection of the elocity a = t /, whee t is the tangential speed. t (towad cente of cicle) a a The diection of the centipetal acceleation is towad the cente of the cicle. a total a t tan a PHYS.1410 Lectue 11 Danylo Depatment of Physics and Applied Physics
4 Let s simplify ou life Unifom Cicula Motion In unifom cicula motion the speed is constant =const o t =const Then, the tangential acceleation a t =0 Then, the centipetal acceleation is not zeo because diection of the elocity changes tan a a tan a tan The magnitude of the centipetal acceleation is constant fo unifom cicula motion: t a const PHYS.1410 Lectue 11 Danylo Depatment of Physics and Applied Physics
5 The best coodinate system fo a Unifom Cicula Motion When descibing cicula motion, it is conenient to define a moing tz-coodinate system. The oigin moes along with a cetain paticle moing in a cicula path. t tan The -axis (adial) points fom the paticle towad the cente of the cicle. a The t-axis (tangential) is tangent to the cicle, pointing in the ccw diection. The z-axis is pependicula to the plane of motion. PHYS.1410 Lectue 11 Danylo Depatment of Physics and Applied Physics
6 If thee is an acceleation, thee must be a foce Unifom Cicula Motion The figue shows a paticle in unifom cicula motion. If thee is an acceleation, thee must be a foce (N. nd law) tan t a The net foce must point in the adial diection, towad the cente of the cicle. Fo an object to be in unifom cicula motion, thee must be a net foce acting on it adially inwads. This centipetal foce is not a new foce. This can be any one of the foces we hae aleady encounteed: tension, gaity, nomal foce, fiction, tan F net F net PHYS.1410 Lectue 11 Danylo Depatment of Physics and Applied Physics
7 ConcepTest Missing Link A Ping-Pong ball is shot into a cicula tube that is lying flat (hoizontal) on a tabletop. When the Ping-Pong ball leaes the tack, which path will it follow? Once the ball leaes the tube, thee is no longe a foce to keep it going in a cicle. Theefoe, it simply continues in a staight line, as Newton s Fist Law equies! Follow-up: What physical foce poides the centipetal acceleation?
8 Examples. Wall of death F f N N F ma N m elocity of the motobike - adius of the cicle Nomal foce poides the centipetal acceleation Bike going in a cicle: the wall exets an inwad foce (nomal foce) on a bike to make it moe in a cicle. PHYS.1410 Lectue 11 Danylo Depatment of Physics and Applied Physics
9 Examples. Hamme Thowe. T F ma T m A hamme going in a cicle: the cod exets an inwad foce (tension) on a hamme to make it moe in a cicle. Tension poides the centipetal acceleation PHYS.1410 Lectue 11 Danylo Depatment of Physics and Applied Physics
10 Examples. Ca on a cicula oad. N a Ca going in a cicle: the oad exets an inwad foce (fiction) on a ca to make it moe in a cicle. Fiction poides the centipetal acceleation F ma PHYS.1410 Lectue 11 Danylo Depatment of Physics and Applied Physics m f s f s elocity of the ca - adius of the cicle Out of these two equations you can get anything you need
11 ConcepTest You die you ca too fast aound a cue and the ca stats to skid. What is the coect desciption of this situation? Aound the Cue A) ca s engine is not stong enough to keep the ca fom being pushed out B) fiction between ties and oad is not stong enough to keep ca in a cicle C) ca is too heay to make the tun D) a dee caused you to skid E) none of the aboe The fiction foce between ties and oad poides the centipetal foce that keeps the ca moing in a cicle. If this foce is m f s too small, the ca continues in a staight line! Follow-up: What could be done to the oad o ca to peent skidding?
12 Examples. Banked cue But sometimes, fiction foce is not enough to keep a ca on a cicula oad. Banking the cue can help to keep cas fom skidding. PHYS.1410 Lectue 11 Danylo Depatment of Physics and Applied Physics
13 Banked Cues (solution) Ncos z F z = Ncos = 0 z N Nsin F = Nsin = ma a = / Nsinm / Ncos Take a atio Independent of object mass!!! tan /g component of nomal foce poides the centipetal acceleation PHYS.1410 Lectue 11 Danylo Depatment of Physics and Applied Physics
14 Example: Loop the Loop PHYS.1410 Lectue 11 Danylo Depatment of Physics and Applied Physics
15 PHYS.1410 Lectue 11 Danylo Depatment of Physics and Applied Physics Loop the Loop To make the loop-the-loop at a constant speed, what minimum speed does the motocycle need? N N 1 N F m ma m N a When N=0 (feels like no weight), then speed is minimum g
16 PHYS.1410 Lectue 11 Danylo Depatment of Physics and Applied Physics Loop the Loop Appaent weight at the bottom, point 1? N 1 1 N N F ma m m a Thus, N >. You would feel heaie (simila to an eleato)
17 ConcepTest Going in Cicles You e on a Feis wheel moing in a etical cicle. When the Feis wheel is at A) N emains equal to est, the nomal foce N exeted by you B) N is smalle than seat is equal to you weight. How C) N is lage than does N change at the top of the Feis D) none of the aboe wheel when you ae in motion? N m m N You ae in cicula motion, so thee has to be a centipetal foce pointing inwad. At the top, the only two foces ae (down) and N (up), so N must be smalle than. Follow-up: Whee is N lage than?
18 Example: Conical pendulum z F z T z 0 (1) a T T T z T F T T Sin m ma () component of tension poides the centipetal acceleation PHYS.1410 Lectue 11 Danylo Depatment of Physics and Applied Physics
19 PHYS.1410 Lectue 11 Danylo Depatment of Physics and Applied Physics Thank you See you on Wednesday
20 ConcepTest 4 Going in Cicles II A skie goes oe a small ound hill with adius. Because she is in cicula motion, thee has to be a centipetal foce. At the top of the hill, what is F c of the skie equal to? F c points towad the cente of the cicle (i.e., downwad in this case). The weight ecto points down and the nomal foce (exeted by the hill) points up. The magnitude of the net foce, theefoe, is F c = N. A) F c = N + B) F c = N C) F c = T + N D) F c = N E) F c = N Follow-up: What happens when the skie goes into a small dip?
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