Transcript Chapter 9 Circular Motion

Chapter 9 Circular Motion
Conceptual Physics Chapter 9
1
Rotation and Revolution
¤ Any object that is turning does so about
an imaginary straight line called the
axis.
¤ If the axis is located within the turning
body (internal), the motion is called a
rotation.
¤ If the axis is located outside of the
turning body (external), the motion is
called a revolution.
Conceptual Physics Chapter 10
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Rotation and Revolution
REVOLUTION
ROTATION
WhileThe
the disc
bug ROTATES
REVOLVES
aboutabout
an external
its internal
axis
axis
Conceptual Physics Chapter 10
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Tangential Speed
¤ Linear speed is the distance traveled
per unit time.
s =
r
d
t
2πr
=
T
The
If antangential
time
object
it takes
travels
speed
tocan
once
ofbe
circumference
complete
the
around
body
a circular
is
precisely
thewhere
linear
path,
one
found
by
2πr,
r isit
circular
speed
travels
along
apath
distance
is
called
circular
equal
the
radius
ofthe
the
circle.
the
path.
to the
period
circumference
and is
of
represented
the circle. by T.
Conceptual Physics Chapter 10
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Tangential Speed
The linear speed
of the ball at any
given instant is
always directed
tangent to the
circular path.
Conceptual Physics Chapter 10
5
Rotational Speed
¤ The rotational speed or angular speed is
the number of rotations per unit time.
¤ Rotational speed is commonly measured
in RPM (rotations/revolutions per
minute).
¤ We use the Greek letter omega (ω) to
represent rotational speed.
¤ Example: ω = 30 RPM
Conceptual Physics Chapter 10
6
Rotational Speed
The tangential
Two
objects placed
speedonand
the
samerotational
the
rotating platform
speed are
will haveby
related
the same
rotational speed.
v = r·ω
The object furthest
…and
the center
greater
the
The
the platform
fromfaster
the
of
radial
distance,
the
spins,
the
greater
the
rotation will have the
tangential
speed
will speed.
be at
greater
tangential
greatestthe
tangential
any point
the platform.
speed
willon
be.
Conceptual Physics Chapter 10
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Question
On a merry-go-round, the horses along the
outer rail are located three times farther
from the axis of rotation than the horses
along the inner rail. If a boy sitting on one of
the inner horses has a rotational speed of 4
RPM and a tangential speed of 2 m/s, what
will be the tangential speed and rotational
speed of his sister sitting on one of the outer
horses?
Conceptual Physics Chapter 10
8
Centripetal Force
This
In
order
force
for
must
an be
object totoward
directed
move along
the
a circular
center
of path,
the circle
there
and
it must
is called
be athe
force actingforce
centripetal
on the
object to change
(centripetal
means
its
direction of motion.
“center-seeking”).
Conceptual Physics Chapter 10
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Centripetal Force
¤ The sideways acting friction between the
tires of a car and the road keeps the car
moving safely along a circular curve.
¤ The car door exerts
an inward normal
force on the
passenger in a
vehicle that is
rounding a left-hand
turn.
Conceptual Physics Chapter 10
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Centripetal Force
If the road is
slick or friction is
not great enough,
the car will have
a tendency to
skid off tangent
to the curve.
Conceptual Physics Chapter 10
11
Centripetal Force
The earth exerts
an inward
gravitational force
on the moon as it
travels along its
circular orbit about
the earth.
Conceptual Physics Chapter 10
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Centripetal Force
¤ The spinning drum in a washing machine
exerts an inward force on the clothes
inside of it.
¤ The holes in the spinning
drum prevent it from
exerting an inward force on
the water and the water will
consequently fly off tangent
to the drum wall.
Conceptual Physics Chapter 10
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Centripetal Force
Txconical
A
Only
The
Since
isvector
two
the
thenet
forces
pendulum
bob
T force
can
doesn’t
act
beon
isona
bob bob–the
resolved
accelerate
the
bob:
held mg,
into
in vertically,
a centripetal
the
circular
twoforce
pathnet
due
perpendicular
the
force!
to
bygravity,
force
a string
inand
theT,
attached
tension
components,
vertical
in
direction
above.
theTstring.
is
x The
string Therefore
(horizontal),
zero.
of a conical
and TTyy
pendulum
(vertical).
must
be equal
sweeps
andout a
cone.
opposite
to mg.
Conceptual Physics Chapter 10
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Centripetal Force
The vertical
Skidding
Suppose
Only
two the
is
forces
reduced
component
speed
actof
onthe
high-speed
the
ofvehicle
the
vehicle,
normal
is the
roadsthat
such
weight,
force
n
by
is
banking
the
equal
and
vehicle
the
and
thenormal
opposite
turns.
has noforce
This
tendency
to mg,
nis (the
and
ymg,
called
to
support
the
slide
horizontal
superelevation.
down
forcethe
of
component
the
curve
road
The
orof
surface).
up
inward
the
thenormal
curve.
component
force
nx speed,
is the
of the
centripetal
normal
force
force
thatin
to
At that
friction
plays
no adds
role
friction
keeps
the
tovehicle
create
in
a on
greater
a circular
centripetal
path.
keeping
the
vehicle
the track.
force.
Conceptual Physics Chapter 10
15
Centripetal Force
¤ The centripetal force prevents an object
from continuing
along a straight
line. When
¤ There
is no centrifugal
(outward)
force!
the centripetal force vanishes or is reduced,
the object will fly off tangent to the circular
path.
Conceptual Physics Chapter 10
16
Centripetal Force
¤ Centripetal force is not a new type of
force. It is any force that happens to
cause an object to move along a circular
path. It can be provided by gravity,
friction, tension, normal force,
electrical force or any combination of
these.
Conceptual Physics Chapter 10
17
Centripetal Acceleration
¤ Since a body undergoing uniform
circular motion maintains a constant
speed, we must find the acceleration of
this body using
v2
ac =
r
¤ This is called the centripetal
acceleration.
Conceptual Physics Chapter 10
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Centripetal Acceleration
¤ The centripetal acceleration and the
centripetal force are related by
Newton’s second law:
Fc = mac
¤ Both the force that causes circular
motion and the acceleration that results
will always be directed inward.
Conceptual Physics Chapter 10
19
Centripetal Acceleration
Although the speed of
an object undergoing
uniform circular
motion remains
constant, the body
accelerates.
The velocity and acceleration vectors
are always perpendicular to each other.
Conceptual Physics Chapter 10
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Centripetal Force
This string
Suppose
The
same
a spinning
pulls
ladybugon
inward
motion
can
is the
placed
be can
in the
and
used
the
tobottom
generate
bottom
ofofa
a cancan
the
simulated
being
pulls
gravity
inward
whirled
on
in
space.
the feet
in a of the
circle.
ladybug.
Conceptual Physics Chapter 10
Centripetal Force
21
Simulated Gravity
Even though a space
station may be in free
fall, the occupants of the
space station feel a
simulated gravity from
the spinning motion.
At the correct rotational speed this
microgravity will feel identical to the
gravitational pull on earth.
Conceptual Physics Chapter 10
22
Simulated Gravity
Space stations can
either be of a
modest radius with a
rather large
rotational speed or
could be larger to
allow for a reduced
rotational speed.
Conceptual Physics Chapter 10
23
Simulated Gravity
Theproduce
To
effect of
a the
rotational gravity
simulated
speed that
could be
varies
directly
acclimated
with
to by
the
distance
most humans,
from
the axis
spaceand
station
with
would
the
rotational
have to be
speed
nearly
of
the 2
space
km instation.
diameter.
Conceptual Physics Chapter 10
24
Question
How would one’s weight be affected if
the earth were to begin spinning faster
on its axis?
Conceptual Physics Chapter 10
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