physics unit 3: circular & rotational motion. circular motion uniform circular motion period, t:...
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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