PHYSICS UNIT 3: CIRCULAR & ROTATIONAL MOTION

CIRCULAR MOTION Uniform Circular

Motion period, T: time for one

complete revolution, unit: s speed is constant

v = 2r/T(r: radius) velocity is constantly

changing (because direction is changing)

CIRCULAR MOTION all turning

objects have centripetal (center- seeking) acceleration

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/rany 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 (center- fleeing) force pulling on objects

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

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”

PHYSICS

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

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/r

2

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/r

2

Also known as the gravitational field strength 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 = 2r/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

PHYSICS

UNIT 3: CIRCULAR & ROTATIONAL MOTION

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

ROTATIONAL MOTION angular acceleration, = /t: rate of

change in rotation, unit: rad/s2

Rotational Motion & Circular Motion for any point on a spinning object:

v = r ac = r2

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)

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

F1

d1

F2

d2

F2d2 = F1d1

PHYSICS

UNIT 3: CIRCULAR & ROTATIONAL MOTION

UNIT 3 REVIEW

v = 2r/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

= /t = /t v = rac = r2

= Fdsin tc = tcc