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PHYSICS UNIT 3: CIRCULAR & ROTATIONAL MOTION

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CIRCULAR MOTION Uniform Circular Motion period, T: time for one complete revolution, unit: s speed is constant v = 2 r/T (r: radius) velocity is constantly changing (because direction is changing)

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CIRCULAR MOTION all turning objects have centripetal (center- seeking) acceleration

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CIRCULAR MOTION centripetal acceleration, a c = v 2 /r the greater the speed, the greater the centripetal acceleration the smaller the radius of the turn, the greater the centripetal acceleration a centripetal acceleration requires a centripetal force

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CIRCULAR MOTION no centrip etal force = no turning (linear motion)

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CIRCULAR MOTION centripetal force, F c = mv 2 /r any force can be a centripetal force: gravity (planets & moons), friction (car turning a corner), tension (ball on a string), etc.

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CIRCULAR MOTION Frames of Reference - inside a turning object, there seems to be a centrifugal (center- fleeing) force pulling on objects

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CIRCULAR MOTION Frames of Reference - outside the turning object, we see objects inside move in a straight line (inertia), until they get pulled into the turn by centripetal force

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CIRCULAR MOTION centrifugal force only exists within the turning object’s frame of reference - it is a fictitious force

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CIRCULAR MOTION Frames of Reference - things moving on a rotating object seem to be made to turn by the “coriolis force”

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PHYSICS UNIT 3: CIRCULAR & ROTATIONAL MOTION

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QUIZ 3.1 A 50 kg child on a merry-go-round sits 2.0 m from the center and makes 2.0 complete revolution every second. (a) Find the child's period. (b) Find the child's tangential speed. (c) Find the child's centripetal acceleration. (d) Find the centripetal force on the child. v = 2 r/T a c = v 2 /r F c = mv 2 /r

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PHYSICS UNIT 3: CIRCULAR & ROTATIONAL MOTION

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UNIVERSAL GRAVITATION Newton's Law of Universal Gravitation: masses attract gravity force is proportional to each mass twice the mass = twice the force gravity force is inversely proportional to the square of the distance between the masses twice the distance = ¼ the force distance measured from center of mass : point on a body around which mass is balanced

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UNIVERSAL GRAVITATION Newton's Law of Universal Gravitation: F g = Gm 1 m 2 /r 2 F G : force of gravity, m: mass, r: distance between masses G: universal gravitational constant, 6.67× Nm 2 /kg 2 gravity is only significant for very large masses

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UNIVERSAL GRAVITATION acceleration due to gravity, g = Gm e /r 2 Also known as the gravitational field strength m e : earth's mass (5.97×10 24 kg) r: distance from earth’s center (6.38×10 6 m + altitude) g is only 9.80 m/s 2 at sea level – it decreases as altitude increases g is different on other planets & moons (it depends on the planet’s mass and radius)

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UNIVERSAL GRAVITATION Orbits: gravity provides the centripetal force stable orbit: F c = F g orbit speed v = √Gm e /r orbit period T = 2 r/v geosynchronous orbit: T = 24.0 hrs, satellite stays over same position on earth

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UNIVERSAL GRAVITATION Orbits always falling but never reaching the ground "Weightlessness" is NOT gravity-less no gravity = no orbit weightless is no normal force

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PHYSICS UNIT 3: CIRCULAR & ROTATIONAL MOTION

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ROTATIONAL MOTION Rotational Motion: rotation around an internal axis angle, : how much an object has rotated, unit: radian (rad) 2 rad = 360º = 1 revolution (rev) angular velocity, = /t : rate of rotation, unit: rad/s frequency: revolutions per second, unit: Hertz, Hz 1 Hz = 1 rev/s = 2 rad/s

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ROTATIONAL MOTION angular acceleration, = /t: rate of change in rotation, unit: rad/s 2 Rotational Motion & Circular Motion for any point on a spinning object: v = r a c = r 2

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ROTATIONAL MOTION torque, : rotating effect of a force, unit: Nm = Fdsin d: "torque arm" or "lever arm“ q: angle between F and d torque direction: clockwise (c) or counterclockwise (cc)

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ROTATIONAL MOTION Torque is zero when = 0º or 180º Torque is maximum when = 90º

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ROTATIONAL MOTION Newton's Laws for Rotary Motion A spinning object keeps spinning with constant angular velocity unless a net torque acts on it A net torque causes an angular acceleration For every action torque, there is an equal and opposite reaction torque

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ROTATIONAL MOTION Rotational Equilibrium: object is balanced, or moves with constant angular velocity, due to no net torque t c = t cc F1F1 d1d1 F2F2 d2d2 F 2 d 2 = F 1 d 1

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PHYSICS UNIT 3: CIRCULAR & ROTATIONAL MOTION

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UNIT 3 REVIEW v = 2 r/T a c = v 2 /rF c = mv 2 /r F g = Gm 1 m 2 /r 2 G = 6.67× Nm 2 /kg 2 g = Gm p /r 2 v = √Gm p /r m e = 5.97×10 24 kgr e = 6.38×10 6 m = /t = /t v = r a c = r 2 = Fdsin t c = t cc

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