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Circular Motion Chapter 7.3 Motion & Forces • What you already know: – Velocity – a measure of the change in over with . – Mass – A measure of the amount of an object contains. – Acceleration – A measure of the change in over change in . – Force – A or that is equal to the mass of the object multiplied by its acceleration (F = _____). Uniform Circular Motion • Uniform circular motion is defined by any object that is moving at in a circular path. – Determining : » The distance an object moving in a circular path is equal to the (__ = _____). » The time it takes an object to complete one revolution is called the (___). » It then follows that the speed of an object moving in a circular path can be determined by: v= Uniform Circular Motion • If an object is moving at constant speed in a circular path, can it be accelerating? – » Although the speed may be , the is . v » If is changing over time, then the must be changing. » is the change in over (___ = ___). » If the is changing over time, then the object must be . v v v Circular Motion – Instantaneous Velocity • Note that the vector is at the vector and at any given point along the circle. to to the circle v2 r2 r1 r2 r1 r v1 v = r/t Circular Motion – Centripetal Acceleration (ac) • The of an object moving in a circular path always __________ ____________ _____ __________ ___ ____ ___________, and is perpendicular to the velocity vector. v2 -v1 v2 v a r v1 v a = v/ t Centripetal Acceleration • The angle between r1 and r2 is the same as the angle between v1 and v2. – Therefore, the triangles these vectors make are such that: = – If you divide both sides by ___: = – Where : » = v and =a – Hence: = and = Centripetal Acceleration • An alternative representation for centripetal acceleration can be derived using the and period of . »d= »v= – Substituting into ac = » ac = » ac = Circular Motion – Force • To make an object move in a circular path, an must act or at right angles to its of . • This force is called . direction of velocity Direction of required to make object move in a circular path ( ) Centripetal Force • Centripetal force is affected by: – The – The – The of the object (___). of the object around the circle (___). of the circle (___). • Using Newton’s 2nd Law of Motion (Fc = mac), centripetal force is mathematically represented as follows: Fc Fc Note: Centripetal force is an “ ” force How the Factors Affect Centripetal Motion • Which graph shows the proper relationship with respect to force: – Force vs. Mass. Speed – Force vs. Speed. Radius – Force vs. Radius. Mass Objects that travel in circular paths. What is the cause of the force? • The Earth – Sun System: – . • A racecar traveling around a turn on the racetrack: – . • An athlete throwing the hammer: – . The path of objects. • If the centripetal force were suddenly removed from an object moving in a circular path, what trajectory (or path) would it follow? Which Path? (a) (b) (c) Which Path? •Why does the object travel in a straight path once the centripetal force is gone? – Because of – An object in wants to in at in a . – If the is removed, the object will continue in a straight path. Example #1: • A 1.5 kg cart moves in a circular path of 1.3 meter radius at a constant speed of 2.0 m/s. – Determine the magnitude of the centripetal acceleration. – Determine the magnitude of the centripetal force. – Determine the period. Example #1: (cont.) • Centripetal Acceleration: ac = • Centripetal Force: Fc = • Period: T=