1. ___________ Circular Motion (UCM) occurs when
an object moves in a circle at __________________
Uniform
constant speed
rotation
____________
axis
_____________
axis
revolution
A. The 2 types of "Turning Around:"
____________: circular motion around an axis
that is ______________________
rotation
within an object
____________: circular motion around an axis
that is ______________________
revolution
outside of an object

2. B. Two types of Rotational/Revolutionary Speeds:
1. ____________ speed w ("omega")
 _________ for all points on a solid object
 units: _____________ , rpm’s, etc
angular
same
radians/s
___________ speed v
 depends on ______________________ of
rotation or revolution
 units: _______, mph, etc
 v = ______ =_________
 In Regents physics, ______________ is the
only type of speed we deal with
linear
distance from axis
m/s
d/t
2pr/t
linear v

3. r Ex: Earth Everywhere on Earth, the __________speed is the same:
angular r
w = _____________
3600/24h
NYS latitude
2p radians
w = _____________
24 x 3600 sec r
equator
But _________ speed
v = __________ is
greatest at the
______________ and
zero at the _________ .
linear
2pr/t
equator
rotation
axis
poles
Rockets are launched from ____________
because its _________________________________
Florida
linear speed is greatest

4. Linear velocity is always ___________ to the
circle in the _____________ of motion.
tangent
direction
Ex: _____________ (CW)
uniform circular motion:
clockwise v v 1 2 v 8 v 7 3 v v 6 4 5 v v

5. Ex: __________________ (CCW) uniform circular motion: counterclockwise
NOTICE:
In _________ CW
and CCW motion:
The __________
(_____________ of v)
remains constant.
The ___________
of v is changing.
Because of this,
the object must be
__________________
both v v
speed
magnitude 1 v 2 8 v 3 7
direction v 6 v 4 5 v v
accelerating

6. D. The direction of _________________ during UCM acceleration Δv/t
From a = _______
a has the same
direction as ____ . vi 1 Δv Δv vf 2
where Δv = =
vf – vi
vf + (-vi) vf Δv
-vi
a is directed towards the circle’s _____________.
It is called ___________________ acceleration: ac.
It occurs b/c the velocity _______________________.
center
centripetal
changes direction

7. Ex: Direction of ____ for ____ and ______motion CW CCWac
Ex: Direction of ____ for ____ and ______motion CW
CCW 1 v v 1 v ac ac v ac ac 3 7 3 7 ac ac v ac ac v v 5 5 v
Notice:
Even though a is always ____________________,
it is always _____________________ in both cases.
The angle between v and ac is always _______ .
changing direction
towards the center
900

8. E. The _______________ of ac is given by:
magnitude
E. The _______________ of ac is given by:
ac =
v2/r
units of ac = [ ]2 / [ ] = v r
(m/s)2 / m
m2/s2 / m
m/s2 ac ac ac
~v2
~ 1 r
independent v r m

9. The magnitude of Fc is given by: mac m·v2/r units of Fc = =
F. What causes a?
What causes ac?
force F
centripetal force Fc.
Fc = =
The magnitude of Fc is given by:
mac
m·v2/r
units of Fc = =
[ ] [ ]2 / [ ] m v r
(kg)
(m/s)2 / m
kg m2/s2 /m
kg m/s2
= N Fc Fc Fc
~v2
~ 1 r ~m r m v

10. G. Direction of ____ for ____ and ______ motion CW CCWFc
G. Direction of ____ for ____ and ______ motion CW
CCW 1 v v 1 v Fc Fc v Fc Fc 3 7 3 Fc Fc 7 v Fc Fc v v v 5 5
1. Although Fc is always ___________________ , it is
always towards the __________. This was also true
for ac, because force F and the a that it __________
are always ____________________________ .
changing direction
center
causes
in the same direction

11. During UCM, the Fc is an _____________ force
and Fnet ___ 0. Remember: _____________ is
changing direction (even though __________ is
constant), and this is an __________________ .
3. Without Fc, the object would move off on a
____________ (in the direction of its ___.)
4. Fc can be provided by many different forces:
____________ holds planets in elliptical orbits.
____________ keeps cars on road during turns
__________________ allows birds to turn in air
_________ keeps rock turning in a circle
________________ keeps rider on loop-d-loop ride
unbalanced ≠
velocity
speed
acceleration
tangent v
gravity
friction
air resistance
string
normal force

12. 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 v ac
5.8 m/s2
Fc = =
mac Fc
(1500 kg)(5.8 m/s2)
8700 N
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?
e/ In which direction would the car move if Fc became 0?
friction