Transcript PHYSICS

PHYSICS UNIT 3: CIRCULAR
& ROTATIONAL MOTION
Circular Motion
Rotation
Revolution
3 Different Kinds of Speed
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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
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Uniform Circular Motion
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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
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all turning
objects have
centripetal
acceleration
(toward the
center of the
turn)
CIRCULAR MOTION
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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
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CIRCULAR MOTION
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no
centrip
etal
force =
no
turning
(linear
motion)
CIRCULAR MOTION
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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
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Frames of
Reference inside a turning
object, there
seems to be a
centrifugal
(outward from the
center) force
CIRCULAR MOTION
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Frames of
Reference outside the
turning object,
we see objects
inside move in a
straight line
(following
st
CIRCULAR MOTION
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centrifugal force
only exists within
the turning
object’s frame of
reference - it is a
fictitious force
CIRCULAR MOTION
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Frames of
Reference things
moving on a
rotating
object seem
to be made
to turn by
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.
PHYSICS
UNIT 3: CIRCULAR &
ROTATIONAL MOTION
UNIVERSAL GRAVITATION
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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
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distance measured from center of mass:
point on a body around which mass is
UNIVERSAL GRAVITATION
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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
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UNIVERSAL GRAVITATION
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acceleration due to gravity, g = Gme/r2
me: earth's mass (5.97×1024 kg)
6
 r: distance from earth’s center (6.38×10 m
+ altitude)
2
 g is only 9.80 m/s 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
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Orbits: gravity provides the centripetal
force
stable orbit: Fc = Fg
 orbit speed v = √Gm /r
e
 orbit period T = 2pr/v
 geosynchronous orbit: T = 24.0 hrs,
satellite stays over same position on
earth
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UNIVERSAL GRAVITATION
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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
ROTATIONAL MOTION
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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:
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ROTATIONAL MOTION
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angular acceleration, a= Dw/t: rate of
change in rotation, unit: rad/s2
Rotational Motion & Circular Motion
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for any point on a spinning object:
 v = rw
2
 a = rw
c
ROTATIONAL MOTION
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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:
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ROTATIONAL MOTION
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Torque is zero when q = 0º or 180º
Torque is maximum when q = 90º
ROTATIONAL MOTION
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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
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Rotational Equilibrium: object is
balanced, or moves with constant
angular velocity, due to no net torque
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Stc = Stcc
d1
F1
d2
F2
F2d2 = F1d1
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