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CIRCULAR MOTION
Section 6.2
Pg 153-156
OBJECTIVES
 Explain
why an object moving in a circle at
constant speed is accelerating.
 Describe
how centripetal acceleration
depends upon the object’s speed and the
radius of the circle.
 Identify
the force that causes the centripetal
acceleration
 Explain
the “nonexistent Force” (inertia)
UNIFORM CIRCULAR MOTION
 Movement
of an object around a
circle of fixed radius at constant
speed
Question: Why does it state
constant speed instead of
constant velocity?
Notice the direction of velocity is
different at different points in the
circle; thus velocity is NOT constant.
VELOCITY AROUND A CIRCLE

Since direction is constantly changing, we look
only at the magnitude of the velocity (speed)
𝒅𝒊𝒔𝒕𝒂𝒏𝒄𝒆
𝒔𝒑𝒆𝒆𝒅 =
𝒕𝒊𝒎𝒆
𝟐𝝅𝒓
𝒗=
𝑻
Distance around a circle is called the
CIRCUMFERENCE.
Time taken to go around the circle once is
called PERIOD.
v = velocity (m/s)
r = radius (m)
T = period (s)
UNIFORM CIRCULAR MOTION

At any given point, velocity is
always tangent to the circle.

Therefore, velocity is always
changing
An object that is changing its
velocity must be experiencing
an acceleration.
 Accelerations are caused by
forces, therefore, there must be
a force acting on the object in
order to keep it going in a circle.

Think back to the bowling ball lab!! What did you need to do
to the ball to keep it going around in a circle?
CENTRIPETAL ACCELERATION
Since you needed to apply a force towards
the center of the circle in the bowling ball
lab, the acceleration must also point
towards the center of the circle.

Centripetal Acceleration
Direction: Always points to the center of the circle
 Magnitude: related to the velocity squared and inversely
related to the radius of the circle.

𝒗𝟐
𝒂𝒄 =
𝒓

ac = centripetal acceleration (m/s2)
v = velocity (m/s)
r = radius (m)
Centripetal acceleration and velocity are always
perpendicular to each other.
CENTRIPETAL FORCE
Describes the net force toward the
center of the circle. It is NOT a type
of force, but in actuality, describing
how a force is acting.

Newton’s Second Law gets rewritten as the net
centripetal force is equal to the mass of the object
times the centripetal acceleration of the object.
𝑭𝑪 = 𝒎𝒂𝒄
Fc = Centripetal Force (N)
ac = centripetal acceleration (m/s2)
m = mass (kg)
CENTRIPETAL FORCES

Lets take a look at a Ferris wheel and draw a FBD at
four points: TOP
FN
Fg ac
•
•
•
•
FN
•
Fg
TOP
Normal force points up (-)
Weight points down (+)
Centripetal acceleration points
into the circle (DOWN)
Therefore, the weight force
must be greater than the
normal force up.
You feel LIGHTER at the top
of the Ferris wheel
CENTRIPETAL FORCES

Lets take a look at a Ferris wheel and draw a FBD at
four points: BOTTOM
Fg ac
•
•
•
•
FN
ac
Fg
•
BOTTOM
Normal force points up (+)
Weight points down (-)
Centripetal acceleration
points into the circle (UP)
Therefore, the normal force
up must be greater than the
weight force down.
You feel HEAVIER at the
bottom of the Ferris wheel
CENTRIPETAL FORCES

Lets take a look at a Ferris wheel and draw a FBD at
four points: SIDES
FN
FN
ac
Fg
ac
•
•
•
•
Fg
•
•
SIDES
Normal force points up
Weight points down
Centripetal acceleration
points into the circle
(LEFT/RIGHT)
Therefore, neither the
normal force nor the weight
force act centripetally.
Vertically in equilibrium –
normal force must be equal
to weight force.
You feel YOUR TRUE
WEIGHT at the sides of the
Ferris wheel
CENTRIPETAL FORCE

What forces can be seen acting centripetally?
1.
2.
3.
4.
Gravitational Force (vertical circles)
Normal Force (Gravitron, Ferris Wheel)
Tension (String)
Friction (Horizontal circle- car around turn)
CENTRIPETAL FORCES - FBD

Centripetal motion can be identified more
specifically as vertical circular motion or
horizontal circular motion.
HORIZONTAL
VERTICAL
Examples:
Car around a turn,
gravitron, twirling a ball
around in a circle
Examples:
Ferris wheel, air show of jets
doing nose dives
Draw the FBD as a top view
Draw the FBD as a side view
• ONLY forces that point directly into the circle or
directly out of the circle act centripetally.
• Forces pointing into the circle – POSITIVE
• Forces pointing out of the circle - NEGATIVE
NON-EXISTENT FORCE


Take a car making a sharp right turn
A passenger in the car is going to feel like they are
being “pushed” towards the left (outward from the
turn).
Question: Is there a force that is pushing the
passenger to the left when the car is making a right
turn?
 There is no outward force acting on you, it is your
body’s inertia (resistance to change) that keeps your
body from following the car through the turn.
NEWTON’S FIRST LAW – object in motion stays in motion in a
straight line at constant velocity unless acted on by a net force.
CENTRIPETAL FORCE QUESTION
What happens if the centripetal force stops existing?
Does the object continue in a circular path?
If the centripetal force stops existing, then Newton’s First
Law explains that the object will continue in a straight
line at constant velocity until it encounters another force.