Uniform Circular Motion
WE WILL LEARN ABOUT UNIFORM CIRCULAR
MOTION
I WILL USE THE CENTRIPETAL FORCE
EQUATION TO SOLVE FOR DIFFERENT
VARIABLES.
Warm up
Turn in your Hooke’s Law Lab report to the
bin.
2. Take out:
1.




your elevators HW set.
A blank sheet of paper.
Something to write with.
A calculator
 HW quiz will begin after I take attendance and
perform the tension demo from last class.
Elevators Homework Quiz
 Once you finish:
 turn your answers into the top bin
 place the quiz worksheet in the bottom bin
 Pick up a circular motion worksheet
New Topic – Uniform Circular Motion
1.
Have you ever heard of centripetal motion? If so,
explain.
2. Have you ever heard of centrifugal force? If so,
explain.
Circular motion
 Uniform circular motion pertains to objects moving
at a constant speed in a perfectly circular path.
 Circles review:
 How do you find the circumference of a circle?
 Complete questions 1-2 of the class work worksheet
New vocabulary
 Period, T [measured in seconds]
 the time required to travel once through a full cycle
in UCM this means time required to travel one full circle.
 Frequency, f [measured in Hertz, Hz]
 the number of complete cycles an object completes per a given
amount of time
 in UCM this means the number of complete circles an object
completes in 1 second.
Speed in UCM
2𝜋𝜋𝜋𝜋
𝑣𝑣 =
= 2𝜋𝜋𝑟𝑟𝑟𝑟
𝑇𝑇
Complete questions 3-4 of the worksheet
2 different types of velocity
 Angular velocity (ω)– measured in
radians/second
2𝜋𝜋
𝑣𝑣
𝜔𝜔 =
= 2π𝑓𝑓 =
𝑇𝑇
𝑟𝑟
 Linear velocity (v) – measured in meters/second
𝑣𝑣 = 𝑟𝑟𝜔𝜔
Period & frequency practice problems
 Complete questions 5-10 of the worksheet
Centripetal acceleration
2
𝑣𝑣
𝑎𝑎𝑐𝑐 =
𝑟𝑟
Circular motion demo 1
If I swing a ball around on a string and let it go. Which
way will it fly?
Centripetal vs. centrifugal
 There is no such thing as a centrifugal force.
 The fake centrifugal force is a perceived force. It
feels like you are being swing outward, but the
opposite is true.
 In order for an object to travel in a circle, it requires
a net force towards the center of the circle. This is
the centripetal force.
Has anyone ridden a carnival ride called
the Gravitron?
 http://www.youtube.com/watch?v=UMvtizOAtVU&list=PLDJPEToivI
XYnC7jjeq7girHp-Q-8YEQl
 http://www.youtube.com/watch?v=fDz9w50O-AA
Centripetal force
Centripetal force always points towards the center of
the circle
‘centripetal’ means center seeking
The centripetal force is a NET FORCE
The centripetal force is often a force of tension.
Centripetal force
𝑚𝑚𝑣𝑣
𝐹𝐹𝑐𝑐 =
𝑟𝑟
2
Centripetal force
𝑚𝑚𝑣𝑣
𝐹𝐹𝑐𝑐 =
𝑟𝑟
2
Do you feel more centripetal force for a sharper turn or
a wider turn?
Centripetal force
Horizontal circles
 For simplicity, we will start by looking at cases in the
horizontal plane with only one force providing the
centripetal force.
 Example problems: #11, 12, 13
Simulating gravity in outer space
 If there is no force of gravity in outer space, how can
a space ship ‘fake’ a force of gravity so people aren’t
just floating around?
Faking gravity
 A rotating spaceship uses the normal force of the
outer wall to give passengers ‘apparent weight’ just
like in an elevator
 Example problems: #14 & 15
Vertical circles
 If an object is being swung in a vertical circle, there
are two forces acting, tension and gravity.
 At the top, tension and gravity act together to
provide the centripetal force.
 At the bottom, tension has to act against gravity to
provide the centripetal force.
Newton’s Law of Universal Gravitation
𝐺𝐺𝑚𝑚1 𝑚𝑚2
𝐹𝐹𝐺𝐺 =
2
𝑟𝑟
is a centripetal force when applied to planets.
G=6.67 x 10-11 N·m2/kg2
Orbits
 Gravity is supplying the centripetal force to keep
planets, satellites and moons in orbit.
Satellites
A geosynchronous satellite is a satellite that orbits
Earth with the same period and frequency as the
rotation of the earth so it stays in the same location
relative to the surface of the Earth.
There is only one specific altitude that a satellite can
achieve this feat.
Mass of the earth: 5.975 x 1024 kg
Radius of the earth: 6.371 x 106 m
Homework
 Circular HW Set – quiz next class
 Looking ahead: Next 3 classes
 Lab
 Review Day
 Newton’s Laws Test 2