TOPIC 1.5: CIRCULAR MOTION

TOPIC 1.5: CIRCULAR MOTIONS4P-1-19Explain qualitatively why an object moving at constant speed in a circle isaccelerating toward the centre of the circle.S4P-1-20Discuss the centrifugal effects with respect to Newton’s laws.S4P-1-21Draw free-body diagrams of an object moving in uniform circular motion.S4P-1-22Experiment to determine the mathematical relationship between period andfrequency and one or more of the following: centripetal force, mass, and radius.S4P-1-23Derive an equation for the constant speed and acceleration of an object moving in acircle 2π rv2 , a . v TR S4P-1-24Solve problems for an object moving with a constant speed in a circle usinga v 2 2π r ,v , and Fnet ma.RT

Topic 1: Mechanics SENIOR 4 PHYSICSGENERAL LEARNING OUTCOMECONNECTIONStudents will Demonstrate appropriate scientificinquiry skills when seeking answers toquestions (GLO C2)SPECIFIC LEARNING OUTCOMES4P-1-19: Explain qualitatively whyan object moving at a constant speedin a circle is accelerating toward thecentre of the circle.SUGGESTIONS FOR INSTRUCTIONEntry Level KnowledgeClassroom ActivitiesStudents should be familiar with the circumferenceof a circle, Newton’s Second Law, and uniformaccelerated motion.Students build and use accelerometers to observethe effects of various forms of acceleration. Thesedevices are often used when students investigatethe physics of amusement park rides.Notes to the TeacherUniform circular motion is the motion of an objectmoving at a constant speed in a circular path. Theacceleration—centripetal acceleration—toward thecentre of the circle can be explained using thedefinition of acceleration (rate of change ofvelocity) where the direction of the acceleration isthe same as the direction of the change in velocity(see diagram). That is, since the net force is towardthe centre, so is the acceleration.DvFcviFcvfF ma48 – Topic 1.5 Circular Motionvf-v i

SENIOR 4 PHYSICS Topic 1: MechanicsSKILLS AND ATTITUDES OUTCOMES4P-0-2a: Select and use appropriatevisual, numeric, graphical, andsymbolic modes of representationto identify and representrelationships.SUGGESTIONS FOR INSTRUCTIONGENERAL LEARNING OUTCOMECONNECTIONStudents will Demonstrate curiosity, skepticism,creativity, open-mindedness, accuracy,precision, honesty, and persistence, andappreciate their importance as scientificand technological habits of mind(GLO C5)SUGGESTIONS FOR ASSESSMENTTeachingNotesTopic 1.5 Circular Motion – 49F ma

Topic 1: Mechanics SENIOR 4 PHYSICSGENERAL LEARNING OUTCOMECONNECTIONStudents will Evaluate, from a scientific perspective,information and ideas encountered duringinvestigations and in daily life (GLO C8)SPECIFIC LEARNING OUTCOMES4P-1-20: Discuss the centrifugaleffects with respect to Newton’slaws.SUGGESTIONS FOR INSTRUCTIONEntry Level KnowledgeNewton’s laws are covered in Senior 2 Science andSenior 3 Physics.Notes to the TeacherIf you are in the front seat of a car and the carsuddenly turns in a circular path, counterclockwise,you will be “thrown” to the right-hand side of thecar. You will feel as if there is a force moving you.Such a force, which appears to be directed awayfrom the centre of the path, is often called acentrifugal “force.” As the car moves in a circularpath, inertia keeps your body going in a straightline. This path causes you to move to the righthand side of the car, which is turning. Thecentrifugal “force” feels real, but it doesn’t reallyexist. Consequently, most physicists prefer theterm “centrifugal effect” rather than “centrifugalforce.”F ma50 – Topic 1.5 Circular MotionOften, this outward force is attributed to circularmotion. For example, everything on a rotatingplatform behaves as if there was a mysterious forcepulling outwards. Tall objects tend to topple overand small ones try to slide away from the centre.Some people refer to this as centrifugal “force,”but there really is no force at all. Centrifugalmeans “centre-fleeing” or “away from the centre.”Centrifugal “force” can be explained by theabsence of a force to keep the object moving incircular motion. If an object in uniform circularmotion is suddenly released, the object will moveoff in a straight line at a constant speed accordingto Newton’s Law of Inertia. Sometimes, it is usefulto use a frame of reference that is rotating with thesystem. In such a system, the centrifugal “force”appears mathematically. But, when the samesituation is examined from a stationary frame, suchas the ground, it does not exist.

SENIOR 4 PHYSICS Topic 1: MechanicsSKILLS AND ATTITUDES OUTCOMES4P-0-4e: Demonstrate a continuingand more informed interest inscience and science-related issues.GENERAL LEARNING OUTCOMECONNECTIONStudents will Understand how stability, motion,forces, and energy transfers andtransformations play a role in a widerange of natural and constructed contexts(GLO D4)SUGGESTIONS FOR INSTRUCTIONSUGGESTIONS FOR ASSESSMENTClassroom ActivitiesHave students predict the path of an object movingin uniform circular motion when it is suddenlyreleased. The object could be attached to the end ofstring or a marble rolling around the inside of a icecream pail lid with one portion of the lid removed.? ? ?DemonstrationA centrifuge is a useful device for separatingsubstances; for example, a cream separator on afarm or a blood centrifuge in the hospital. A simplecentrifuge can be made with an old turntable, somecups, and some objects such as ping pong balls(see Appendix 1.9 for details).Topic 1.5 Circular Motion – 51F ma

Topic 1: Mechanics SENIOR 4 PHYSICSGENERAL LEARNING OUTCOMECONNECTIONStudents will Recognize that scientific knowledge isbased on evidence, models, andexplanations, and evolves as newevidence appears and newconceptualizations develop (GLO A2)SPECIFIC LEARNING OUTCOMESKILLS AND ATTITUDES OUTCOMESS4P-1-21: Draw free-body diagramsof an object moving in uniformcircular motion.S4P-0-2h: Analyze problemsusing vectors.Include: Adding and subtractingvectors in straight lines, at rightangles, and at non-orthogonal anglesSUGGESTIONS FOR INSTRUCTIONEntry Level KnowledgeFree-body diagrams are covered in Senior 3Physics.Notes to the TeacherFfStudents can draw free-body diagrams to illustrateforces acting on a sphere or a coin moving in auniform circular motion. In each case, they shouldindicate the force(s) responsible for the centripetalforce. The relative length of the vectorscorresponding to the forces should be drawn toscale.FGSymbols:Fg — WeightFT — TensionFf — FrictionFN — Normal ForceFC — Centripetal ForceFTRotating CoinFNFGRotating SphereF ma52 – Topic 1.5 Circular MotionFN

SENIOR 4 PHYSICS Topic 1: MechanicsSKILLS AND ATTITUDES OUTCOMESS4P-0-2i: Select and integrateinformation obtained from avariety of sources.Include: print, electronic, specialists,or other resource peopleS4P-0-4b: Work co-operatively with agroup to identify priorknowledge, initiate and exchangeideas, propose problems and theirsolution, and carry outinvestigations.SUGGESTIONS FOR INSTRUCTIONGENERAL LEARNING OUTCOMECONNECTIONStudents will Demonstrate appropriate scientificinquiry skills when seeking answers toquestions (GLO C2)SUGGESTIONS FOR ASSESSMENTVisual DisplaysStudents design and construct a model of anamusement park ride. The forces acting aredescribed using a free-body diagram.SUGGESTED LEARNING RESOURCESFNFfGoing in Circles, Activity 30, p 183, Lab Manual,Conceptual Physics, Pearson, 2002FGRotating CylinderTopic 1.5 Circular Motion – 53F ma

Topic 1: Mechanics SENIOR 4 PHYSICSGENERAL LEARNING OUTCOMECONNECTIONStudents will Demonstrate appropriate problem-solvingskills while seeking solutions totechnological challenges (GLO C3)SPECIFIC LEARNING OUTCOMESKILLS AND ATTITUDES OUTCOMESS4P-1-22: Experiment to determinethe mathematical relationshipbetween period and frequency andone or more of the following:centripetal force, mass, and radius.S4P-0-1e: Differentiate betweenhow scientific theories explainnatural phenomena and howscientific laws identify regularitiesand patterns in nature.S4P-0-2a: Select and use appropriatevisual, numeric, graphical, andsymbolic modes of representation toidentify and represent relationships.SUGGESTIONS FOR INSTRUCTIONEntry Level KnowledgeStudents have used graphical analysis toinvestigate mostly linear relationships. In this case,graphical analysis is extended to the power andinverse relationships.Notes to the TeacherThe common approach to investigating therelationships for circular motion is by swinging arubber stopper as shown in the diagram. Severalfactors can be measured, including frequency,period, mass, radius, and force.tubethreadpaper clipmassF ma54 – Topic 1.5 Circular Motion

SENIOR 4 PHYSICS Topic 1: MechanicsSKILLS AND ATTITUDES OUTCOMESS4P-0-2b: Propose problems, statehypotheses, and plan, implement,adapt, or extend procedures to carryout an investigation where required.S4P-0-2c: Formulate operationaldefinitions of major variables orconcepts.S4P-0-2d: Estimate and measure accuratelyusing SI units.S4P-0-2e: Evaluate the relevance,reliability, and adequacy of data anddata-collection methods.Include: discrepancies in data and sourcesof errorS4P-0-2f: Record, organize, and displaydata using an appropriate format.Include: labelled diagrams, tables, graphsGENERAL LEARNING OUTCOMECONNECTIONStudents will Work co-operatively and value the ideasand contributions of others whilecarrying out scientific and technologicalactivities (GLO C7)S4P-0-2g: Develop mathematical modelsinvolving linear, power, and/orinverse relationships among variables.SUGGESTIONS FOR INSTRUCTIONSUGGESTIONS FOR ASSESSMENTLaboratory ReportTeachingNotesStudents collect, organize, and graphicallyillustrate data obtained and submit a lab report.SUGGESTED LEARNING RESOURCESInvestigation 11-B: Verifying the Circular MotionEquation, Physics 12, McGraw-Hill Ryerson, 2003Topic 1.5 Circular Motion – 55F ma

Topic 1: Mechanics SENIOR 4 PHYSICSSPECIFIC LEARNING OUTCOMESGENERAL LEARNING OUTCOMECONNECTIONS4P-1-23: Derive an equation for theconstant speed and acceleration ofan object moving in a circleStudents will Recognize that scientific knowledge isbased on evidence, models, andexplanations, and evolves as newevidence appears and newconceptualizations develop (GLO A2)S4P-1-24: Solve problems for anobject moving with a constant speedin a circle using v 2 2π r , and Fnet ma.a ,v RT 2π rv2 v ,a .TR SUGGESTIONS FOR INSTRUCTIONNotes to the TeacherSince these triangles are similar, the ratio of theThe equation for the constant speed of an objectmoving in a circle is derived from basic principles.We know thatcorresponding sides are equal and, R v v,Rdivide both sides by t to get R v . dv tR tand, for an object moving in a circle, that the pathis the circumference of the circle. That isSince v d 2π R.v a R v, this reduces to and a R v t tand finally a Therefore, v 2π r . v tv2.RTNotice this is a scalar equation; however, thedirection of the acceleration will always be towardthe centre of the circle.2There are several ways to derive a v.RRemind students that vectors can be movedanywhere as long as the magnitude and directiondo not change. Compare the triangles formed from the position vectors R R2 R1 and the velocity vectors v v2 v1 . RRDRRv1Dv2Dv1RDvv2F ma56 – Topic 1.5 Circular Motion