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PHYSICS UNIT 3: CIRCULAR & ROTATIONAL MOTION

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Circular Motion RotationRevolution

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3 Different Kinds of Speed 1. Linear Speed - covering a distance in a time. S=D/t 2. Tangential Speed - speed of something moving in a circular path. V = 2 πr/T (Revolving!) 3. Rotational Speed - the number of rotations in a second. S r = # rot./ second Come up with an example of each.

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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 acceleration (toward the center of the turn)

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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 (outward from the center) 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 (following Newton’s 1 st Law), 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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QUIZ 3.1 A child on a merry-go-round sits 1.5 m from the center and makes 2.0 complete revolutions every second. (a) Find the child's period. (b) Find the child's speed. (c) Find the child's centripetal acceleration. 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, 6.67×10 -11 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 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 = 6.67×10 -11 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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