An object moving in uniform
circular motion is moving in a
circle with a constant speed.
uniform:
not changing in form or character;
remaining the same in all cases and at all
times
uniform speed=constant speed
speed is how fast an object is moving
• An accelerating object is an object that
has a change in velocity.
• Velocity is a vector—which has both
magnitude and direction
– a change in either the magnitude or the
direction (or both) means there is a change in
velocity.
• For this reason, it can be said that an
object moving in a circle at constant
speed is indeed accelerating.
It is accelerating because the
velocity is changing directions.
An object moving in a circle
experiences an acceleration.
This acceleration is directed
TOWARD THE CENTER
of the circle.
For an object moving in a circle,
there must be an inward force
acting upon it in order to cause its
inward acceleration.
This force is called the
Centripetal Force.
the word ‘centripetal’ means “center-seeking”
Newton's First Law of Motion
(the Law of Inertia)
states that….
"... objects in motion tend to stay in
motion with the same speed and the
same direction unless acted upon by
an unbalanced force."
Centripetal Force:
a physical force pushing or pulling
the object towards the center of the
circle.
The word "centripetal" is merely an
adjective used to describe the
direction of the force.
“center-seeking”
Examples of Centripetal Force
As a car makes a turn, the force of friction
acting upon the turned wheels of the car
provide the centripetal force required
for circular motion.
As the moon orbits the Earth, the
force of gravity acting upon the
moon provides the centripetal
force required for circular motion.
As a bucket of water is tied to a
string and spun in a circle, the
force of tension acting upon the
bucket provides the centripetal
force required for circular motion.
Newton’s Second Law
states that….
• an object which experiences an
acceleration must also be
experiencing a net force.
• the direction of the net force always
acts in the same direction as the
acceleration.
The Centripetal Force
causing an object to move
in a circle creates an
acceleration that is
directed toward the center
of the circle.
Equations to find
Centripetal Acceleration:
2
v
a
R
where:
v is velocity
R is radius
T is time
and pi is 3.14
in other
words
4 R
a
2
T
2
Find the Centripetal
Acceleration of a runner
running with a velocity of
8.8 m/s around a track
with a radius of 25 m.
Find the Centripetal
Acceleration of a car
driving around an exit
ramp with a velocity of
15 m/s. Assume the exit
ramp has a radius of 30 m
A dog sits 1.5 m from the center
of a merry-to-round. The merrygo-round is set in motion, and the
dog’s speed is 1.5 m/s. what is
the dog’s centripetal
acceleration?
A rope attaches a tire to an
overhanging tree limb. A girl
swinging on the tire has a
centripetal acceleration of 3.0
2
m/s . If the length of the rope
is 2.1 m, what is the girl’s
speed?
A race car moving along a
circular track has a centripetal
acceleration of 15.4 m/s2. If the
car has a tangential speed of 30
m/s, what is the distance
between the car and the center o
the track?