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Uniform Circular Motion (UCM) occurs when
___________
constant speed
an object moves in a circle at __________________
rotation
____________
axis
_____________
revolution
axis
A. The 2 types of "Turning Around:"
rotation
____________:
circular motion around an axis
that is ______________________
within an object
revolution
____________:
circular motion around an axis
that is ______________________
outside of an object
B. Two types of Rotational/Revolutionary Speeds:
angular
1. ____________
speed w ("omega")
same for all points on a solid object
 _________
radians/s , rpm’s, etc
 units: _____________
linear
2.___________
speed v
distance from axis
 depends on ______________________
of
rotation or revolution
m/s
 units: _______,
mph, etc
d/t =_________
2pr/t
 v = ______
 In Regents physics, ______________
is the
linear v
only type of speed we deal with
Ex: Earth
Everywhere on Earth, the
angular
__________speed
is the
same:
0
r
360 /24h
w = _____________
NYS latitude
equator
rotation
axis
r
2p radians
w = _____________
24 x 3600 sec
But _________
linear speed
2pr/t
v = __________
is
greatest at the
equator
______________
and
poles .
zero at the _________
Florida
Rockets are launched from ____________
because its _________________________________
linear speed is greatest
tangent
C. Linear velocity is always ___________
to the
circle in the _____________
direction of motion.
clockwise (CW)
Ex: _____________
uniform circular motion:
v
v
1
2
8
v
7
v
v
3
6
4
5
v
v
v
counterclockwise
Ex: __________________
(CCW) uniform
circular motion:
v
v
2
v
1
8
3
v
NOTICE:
v
7
6
4
5
v
v
v
both
In _________
CW
and CCW motion:
speed
1. The __________
magnitude of v)
(_____________
remains constant.
2. The direction
___________
of v is changing.
Because of this,
the object must be
accelerating
__________________
acceleration
D. The direction of _________________
during UCM
Δv/t
From a = _______
vi
a has the same
1
Δv
Δv .
vf 2
direction as ____
where Δv =
=
vf – vi
vf + (-vi)
Δv
vf
-vi
center
• a is directed towards the circle’s _____________.
centripetal
• It is called ___________________
acceleration: ac.
changes direction
• It occurs b/c the velocity _______________________.
ac for ____
Ex: Direction of ____
CW and ______motion
CCW
1
v
v
1
v
ac
7
3
ac
ac
v
5
v
ac
ac
v
3
ac
7
ac
v
ac
5
v
Notice:
changing direction
• Even though a is always ____________________,
towards the center in both cases.
it is always _____________________
• The angle between v and ac is always _______
900 .
magnitude of a is given by:
E. The _______________
c
ac = v2/r
units of ac =
[ v ]2 / [ r ]
= (m/s)2 / m
= m2/s2 / m
=
ac
m/s2
ac
~v2
ac
independent
~1
r
v
r
m
F. What causes a?
What causes ac?
force F
centripetal force Fc.
The magnitude of Fc is given by: Fc = mac
= m·v2/r
units of Fc = [ m ] [ v ]2 / [ r ]
= (kg) (m/s)2 / m
= kg m2/s2 /m
= kg m/s2 = N
Fc
Fc
~v2
v
Fc
~1
r
r
~m
m
Fc for ____
G. Direction of ____
CW and ______
CCW motion
1
v
v
1
v
Fc
7
3
Fc
Fc
v
5
v
Fc
Fc
v
3
Fc
Fc
v
7
Fc
5
v
changing direction , it is
1. Although Fc is always ___________________
center
always towards the __________.
This was also true
causes
for ac, because force F and the a that it __________
are always ____________________________
.
in the same direction
unbalanced force
2. During UCM, the Fc is an _____________
velocity
≠ 0. Remember: _____________
and Fnet ___
is
speed
changing direction (even though __________
is
acceleration
constant), and this is an __________________
.
3. Without Fc, the object would move off on a
tangent (in the direction of its ___.)
____________
v
4. Fc can be provided by many different forces:
gravity
• ____________
holds planets in elliptical orbits.
friction
• ____________
keeps cars on road during turns
• __________________
allows birds to turn in air
air resistance
string keeps rock turning in a circle
• _________
normal force keeps rider on loop-d-loop ride
• ________________
Ex: A 1500-kg car moves clockwise in a circle of
radius 25 m at a speed of 12 m/s. Calculate
a/ the centripetal acceleration of the car;
b/ the centripetal force acting on the car.
ac = v2/r
= (12 m/s)2/25 m
= 5.8 m/s2
Fc = mac
= (1500 kg)(5.8 m/s2)
= 8700 N
v
ac
Fc
c/ What direction are v, ac and Fc when the car is at
the point shown?
d/ What provides the Fc that allows the car to turn?
friction
e/ In which direction would the car move if Fc became 0?
Open your Review Book Packet
to
pages 44-45.
Do problems #93-101