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PHYSICS STUDY GUIDE CHAPTER 7: CIRCULAR MOTION TOPICS: • Circular Motion WHAT YOU MUST KNOW • An objects in uniform circular motion moves with constant speed, but changing velocity (direction is always changing). • An objects in uniform circular motion is acceleration • Direction of Centripetal Force • Direction of Centripetal Acceleration • Direction of tangential velocity DEFINITIONS • Circular Motion: Motion of an object that follows a circular path. • Centripetal Force: ANY force that keeps an object moving in a circle • Period (T): Time for an object to complete one entire revolution (rotation, cycle, etc). PHYSICAL QUANTITIES SYMBOL c r T vT aC FC NAME Circumference Radius Period Tangential Velocity Centripetal acceleration Centripetal force UNITS Meters ( m ) Meters ( m ) Seconds ( s ) Meters per second ( m/s ) Meters per second squared ( m/s2 ) Newtons ( N ) MATHEMATICAL MODELS • Circumference • Tangential velocity vT = • Centripetal acceleration • Centripetal Force FEonO = g · m C=2·π·r • Force of Earth 2 · π ·r T v2 ac = r • Force of Static Friction • Coefficient of Static Friction FC = m FS = µS · FN μS = v2 r or v2 (r · g) FC = m ⋅ ac SOURCES OF CENTRIPETAL FORCE The direction of the velocity of an object moving in circular motion is always “tangent to the circle” The direction of the acceleration of an object moving in circular motion is always “towards the center of the circle” The direction of the force of an object moving in circular motion is always “towards the center of the circle” SOURCES OF CENTRIPETAL FORCE SOURCE FORCE DIAGRAM REAL LIFE CONECTION • Dryer • Rollercoaster Normal force • Ferris wheel FC = FN Classroom examples: • Wooden track • Bowling ball + mallet • Pocket of a lacrosse stick • Any vehicle going around a level roundabout or circular track. Force of Static Friction FC = FS • Merry go round Classroom examples: • Record Player FT center FTY • Swings at amusement parks FC = FTX Tension force FC = FT FEonO Classroom examples: • Wiffle ball attached to a string • Plane attached to a string • Amusement park NOTE: FTY holds up the object and balances out FEonO. FC = FTX • Planets around suns Gravitational force • Moons or satellites around planets FC = FG Classroom examples: • Person on Earth’s surface Magnetic force FC = FB N/A • Particle accelerator • Aurora Borealis (Northern Lights) VERTICAL CIRCLES Five cases of an object moving in uniform circular motion in a vertical circle. The system is the person. REPRESEN TATION I II III IV V SKETCH FN FN FC FORCE DIAGRAM FC FC FEonO FN FEonO DIRECTIO N OF CENTRIPE TAL FORCE MATHEMA TICAL MODEL FEonO UP (POSITIVE) DOWN (NEGATIVE) - FSonP – FEonP = - FC + FSonP – FEonP = + FC + FSonP – g·m = + m· DOWN (NEGATIVE) v2 r - FSonP – g·m = - m· UP (POSITIVE) + FSonP – FEonP = + FC + FSonP – FEonP = - FC v2 r + FSonP – g·m = - m· DOWN (NEGATIVE) v2 r + FSonP – g·m = + m· + FSonP – FEonP = - FC v2 r + FSonP – g·m = - m· v2 r