# PHYSICS UNIT 3: CIRCULAR & ROTATIONAL MOTION

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PHYSICS UNIT 3: CIRCULAR & ROTATIONAL MOTION

Circular Motion Rotation Revolution

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 = 2πr/T (Revolving!) 3. Rotational Speed - the number of rotations in a second. Sr= # rot./ second Come up with an example of each.

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

CIRCULAR MOTION all turning objects have centripetal acceleration (toward the center of the turn)

CIRCULAR MOTION centripetal acceleration, ac = v2/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

CIRCULAR MOTION no centripetal force = no turning (linear motion)

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

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

CIRCULAR MOTION Frames of Reference - outside the turning object, we see objects inside move in a straight line (following Newton’s 1st Law), until they get pulled into the turn by centripetal force

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

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

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 = 2pr/T ac = v2/r Fc = mv2/r

UNIT 3: CIRCULAR & ROTATIONAL MOTION
PHYSICS UNIT 3: CIRCULAR & ROTATIONAL MOTION

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

UNIVERSAL GRAVITATION
Newton's Law of Universal Gravitation: Fg = Gm1m2/r2 Fg: force of gravity, m: mass, r: distance between masses G: universal gravitational constant, 6.67×10-11 Nm2/kg2 gravity is only significant for very large masses

UNIVERSAL GRAVITATION
acceleration due to gravity, g = Gme/r2 me: earth's mass (5.97×1024 kg) r: distance from earth’s center (6.38×106 m + altitude) g is only 9.80 m/s2 at sea level – it decreases as altitude increases g is different on other planets & moons (it depends on the planet’s mass and radius)

UNIVERSAL GRAVITATION
Orbits: gravity provides the centripetal force stable orbit: Fc = Fg orbit speed v = √Gme/r orbit period T = 2pr/v geosynchronous orbit: T = 24.0 hrs, satellite stays over same position on earth

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

UNIT 3: CIRCULAR & ROTATIONAL MOTION
PHYSICS UNIT 3: CIRCULAR & ROTATIONAL MOTION

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

ROTATIONAL MOTION Rotational Motion & Circular Motion
angular acceleration, a= Dw/t: rate of change in rotation, unit: rad/s2 Rotational Motion & Circular Motion for any point on a spinning object: v = rw ac = rw2

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

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

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

ROTATIONAL MOTION Rotational Equilibrium: object is balanced, or moves with constant angular velocity, due to no net torque Stc = Stcc F1 F2 d1 d2 F2d2 = F1d1

UNIT 3: CIRCULAR & ROTATIONAL MOTION
PHYSICS UNIT 3: CIRCULAR & ROTATIONAL MOTION

UNIT 3 REVIEW v = 2pr/T ac = v2/r Fc = mv2/r
Fg = Gm1m2/r2 G = 6.67×10-11 Nm2/kg2 g = Gmp/r2 v = √Gmp/r me = 5.97×1024 kg re = 6.38×106 m w = Dq/t a= Dw/t v = rw ac = rw2 t = Fdsinq Stc = Stcc