Add Important Centripetal ore Page: 8 Unit: Rotational Dynami Unit: Rotational Dynami NGSS Standard: N/A Centripetal ore MA Curriulum ramework (006): 1.8 AP Phyi 1 Learning Objetive: 4.D.1.1 Knowledge/Undertanding Goal: Skill: the differene between entripetal and entrifugal fore alulate the entripetal fore of an objet moving in a irle Language Objetive: Undertand and orretly ue the term rotation, entripetal fore, and entrifugal fore. Explain the differene between entripetal fore and entrifugal fore. Lab, Ativitie & Demontration: Swing a buket of water in a irle. Golf ball loop-the-loop. Spin a weight on a tring and have the weight pull up on a ma or pring ale. Note: A we aw previouly, when an objet i moving at a ontant peed around a irle, it diretion keep hanging toward the enter of the irle a it goe around, whih mean there i ontinuou aeleration toward the enter of the irle. Ue thi pae for ummary and/or additional note. AP Phyi 1: Algebra-Baed
Add Important Centripetal ore Page: 83 Beaue aeleration i aued by a net fore (Newton eond law of motion), if there i ontinuou aeleration toward the enter of the irle, then there mut be a ontinuou fore toward the enter of the irle. Thi fore i alled entripetal fore. Unit: Rotational Dynami entripetal fore: the inward fore that keep an objet moving in a irle. If the entripetal fore were removed, the objet would fly away from the irle in a traight line that tart from a point tangent to the irle. Reall that the formula for entripetal aeleration ( a ) i: a v r r Given that = ma, the equation for entripetal fore i therefore: ma mv r mr entrifugal fore : the apparent outward fore felt by an objet that i moving in a irle. Centrifugal fore i tehnially not a fore a we would define it in phyi. Centrifugal fore i atually the inertia of objet reiting motion a they are ontinuouly pulled toward the enter of a irle by entripetal aeleration. Ue thi pae for ummary and/or additional note. AP Phyi 1: Algebra-Baed
Add Important Centripetal ore Page: 84 Unit: Rotational Dynami A an analogy, imagine that you are tanding in an elevator. While the elevator i aelerating upward, the fore between you and the floor of the elevator inreae. An inreae in the normal fore from the floor beaue of the upward aeleration of the elevator feel the ame a an inreae in the downward fore of gravity. Similarly, a ample being pun in a entrifuge i ubjeted to the fore from the bottom of the entrifuge tube a the tube i aelerated toward the enter. The fater the rotation, the tronger the fore. Again, an inreae in the normal fore from the bottom of the entrifuge tube would feel the ame a a downward fore toward the bottom of the entrifuge tube. Sample Problem: Q: A 300 kg roller oater ar reahe the bottom of a hill traveling at a peed of 0 m. If the trak urve upward with a radiu of 50 m, what i the total fore exerted by the trak on the ar? A: The total fore on the ar i the normal fore needed to reit the fore of gravity on the ar (equal to the weight of the ar) plu the entripetal fore exerted on the ar a it move in a irular path. mg (300)(10) 3 000 N g N mv (300)(0) 400 N r 50 3 000 400 5 400 N g Ue thi pae for ummary and/or additional note. AP Phyi 1: Algebra-Baed
Add Important Centripetal ore Page: 85 Unit: Rotational Dynami Q: A 0 g ball attahed to a 60 m long tring i wung in a horizontal irle 80 time per minute. Negleting gravity, what i the tenion in the tring? A: Converting to MKS unit, the ma of the ball i 0.0 kg and the tring i 0.6 m long. T T 80 revolution rad 1min 8 8.38 1min revolution 60 3 mr (0.0)(0.6)(8.38) 0.84 N Homework Problem 1. ind the fore needed to keep a 0.5 kg ball pinning in a 0.70 m radiu irle with an angular veloity of 15 revolution every 10. rad Anwer: 31.1 N. ind the fore of frition needed to keep a 3 000 kg ar traveling with a peed of around a highway exit ramp urve that ha a radiu of 100 m. m Anwer: 14 50 N Ue thi pae for ummary and/or additional note. AP Phyi 1: Algebra-Baed
Add Important Centripetal ore Page: 86 Unit: Rotational Dynami 3. A paenger on an amuement park ride i reting a hill in the ride at 15 m. If the top of the hill ha a radiu of 30 m, what fore will a 50 kg paenger feel from the eat? What fration of the paenger weight i thi? Anwer: 15 N; 1 4 4. A roller oater ha a vertial loop with a 40 m radiu. What peed at the top of the loop will make a 60 kg rider feel weightle? Anwer: 0 m 5. A ride alled The Rotor at Six lag i a ylinder that pin at 56 RPM, whih i enough to tik people to the wall. What fore would a 90 kg rider feel from the wall of the ride, if the ride ha a diameter of 6 m? Anwer: 9 85 N Ue thi pae for ummary and/or additional note. AP Phyi 1: Algebra-Baed