IB Gravity and Circular Motion

PHYSICS UNIT 3: CIRCULAR & ROTATIONAL MOTION

CIRCULAR MOTIONUniform Circular Motionperiod, T: time for one complete revolution, unit: sspeed is constant v = 2pr/T (r: radius)velocity is constantly changing (because direction is changing)

CIRCULAR MOTIONall turning objects have centripetal (center- seeking) acceleration

CIRCULAR MOTIONcentripetal acceleration, ac = v2/rthe greater the speed, the greater the centripetal accelerationthe smaller the radius of the turn, the greater the centripetal acceleration a centripetal acceleration requires a centripetal force

CIRCULAR MOTIONno centripetal force = no turning (linear motion)

CIRCULAR MOTIONcentripetal force, Fc = mv2/rany force can be a centripetal force: gravity (planets & moons), friction (car turning a corner), tension (ball on a string), etc.

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

CIRCULAR MOTIONFrames 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

CIRCULAR MOTIONcentrifugal force only exists within the turning objects frame of reference - it is a fictitious force

CIRCULAR MOTIONFrames of Reference - things moving on a rotating object seem to be made to turn by the coriolis force

PHYSICSUNIT 3: CIRCULAR & ROTATIONAL MOTION

QUIZ 3.1A 50 kg child on a merry-go-round sits 2.0 m from the center and makes 2.0 complete revolutionevery 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 = 2pr/T ac = v2/r Fc = mv2/r

PHYSICSUNIT 3: CIRCULAR & ROTATIONAL MOTION

UNIVERSAL GRAVITATIONNewton's Law of Universal Gravitation: masses attractgravity force is proportional to each masstwice the mass = twice the forcegravity force is inversely proportional to the square of the distance between the massestwice the distance = the forcedistance measured from center of mass: point on a body around which mass is balanced

UNIVERSAL GRAVITATIONNewton's Law of Universal Gravitation: Fg = Gm1m2/r2 FG: force of gravity, m: mass, r: distance between massesG: universal gravitational constant, 6.6710-11 Nm2/kg2gravity is only significant for very large masses

UNIVERSAL GRAVITATIONacceleration due to gravity, g = Gme/r2Also known as the gravitational field strengthme: earth's mass (5.971024 kg)r: distance from earths center (6.38106 m + altitude)g is only 9.80 m/s2 at sea level it decreases as altitude increasesg is different on other planets & moons (it depends on the planets mass and radius)

UNIVERSAL GRAVITATIONOrbits: gravity provides the centripetal forcestable orbit: Fc = Fgorbit speed v = Gme/rorbit period T = 2pr/vgeosynchronous orbit: T = 24.0 hrs, satellite stays over same position on earth

UNIVERSAL GRAVITATIONOrbitsalways falling but never reaching the ground"Weightlessness" is NOT gravity-lessno gravity = no orbitweightless is no normal force

PHYSICSUNIT 3: CIRCULAR & ROTATIONAL MOTION

ROTATIONAL MOTIONRotational Motion: rotation around an internal axisangle, q: how much an object has rotated, unit: radian (rad)2p rad = 360 = 1 revolution (rev)angular velocity, w = Dq/t : rate of rotation, unit: rad/sfrequency: revolutions per second, unit: Hertz, Hz1 Hz = 1 rev/s = 2p rad/s

ROTATIONAL MOTIONangular acceleration, a= Dw/t: rate of change in rotation, unit: rad/s2Rotational Motion & Circular Motionfor any point on a spinning object:v = rwac = rw2

ROTATIONAL MOTIONtorque, t: rotating effect of a force, unit: Nmt = Fdsinq d: "torque arm" or "lever armq: angle between F and dtorque direction: clockwise (c) or counterclockwise (cc)

ROTATIONAL MOTIONTorque is zero when q = 0 or 180Torque is maximum when q = 90

ROTATIONAL MOTIONNewton's Laws for Rotary MotionA spinning object keeps spinning with constant angular velocity unless a net torque acts on itA net torque causes an angular accelerationFor every action torque, there is an equal and opposite reaction torque

ROTATIONAL MOTIONRotational Equilibrium: object is balanced, or moves with constant angular velocity, due to no net torqueStc = StccF2d2 = F1d1

PHYSICSUNIT 3: CIRCULAR & ROTATIONAL MOTION

UNIT 3 REVIEWv = 2pr/T ac = v2/rFc = mv2/rFg = Gm1m2/r2G = 6.6710-11 Nm2/kg2g = Gmp/r2v = Gmp/rme = 5.971024 kgre = 6.38106 mw = Dq/t a= Dw/t v = rwac = rw2t = Fdsinq Stc = Stcc