Circular Motion
 Definition: Uniform Circular motion is the motion of an object traveling at a _____________ (uniform)
speed on a circular path
2.4.1Draw a vector diagram to illustrate that the acceleration of a particle moving with constant speed in
a circle is directed towards the center of the circle.
 _____________ – the straight line around which rotation takes place
 Rotation – a spin around an internal axis. i.e.: a carnival ride or record (big CD)
 Revolution – a spin around an external axis. i.e.: the Earth around the sun
 Speeds for objects in a straight line are called linear (or _____________ ) speeds,
 Linear speeds are a rate at which an object covers a certain distance (v =d/t)
 Ex. Unit – m/s , km/hr , mph
 Can’t express speeds of rotation with a _____________ speed,
 b/c objects at different points on the rotating object have different linear speeds
 Rotational speed
 Expresses the rate at which an object rotates through a portion of a circle ( an angle)
 Ex. Unit --- _____________ ’s
 Are all people on Earth moving at the same speed?? _____________
 Earth is rotating about an axis through its poles
 So that means we are all moving since we are all on the Earth.
 Are some of us moving with a greater LINEAR SPEED than others??
 _____ , closer to the Equator, the faster you are moving…. Closer to poles, the slower you are moving
 Are some of us moving with a greater ROTATIONAL SPEED than others??
 ______ , all people on earth have same rotational speed, because Earth is spinning at the same rate
everywhere
 Velocity was…
v = d/t
 Distance is now the circumference of the circle (2πr)
 Period (T) is the time it takes for one revolution.
 So… Speed = ______________
 This is also called “ _____________ Speed”
 Check Your Neighbor…
 If a meter stick supported at the 0-cm mark swings like a pendulum from your fingers (look at demo),
how fast at any given moment is the 100-cm mark compared to the 50-cm mark?
2.4.2Apply the expression for centripetal acceleration.
 Think about a Ferris wheel. The cars in on the Ferris wheel are in uniform circular motion.
 Even though they have a constant vt, _____________ the cars still have an acceleration?
 This is due to what defines acceleration:
 a = vf – vi
tf - ti
 Because velocity is a vector, acceleration can be changed by the magnitude or direction of the velocity.
 Well, velocity has changed, so centripetal acceleration (ac) will be a little different too
 Centripetal acceleration = (tangential speed)2 / radius of circular path
 The acceleration is still a vector qty, and will always point toward the _____________ of the circle.
2.4.1Draw a vector diagram to illustrate that the acceleration of a particle moving with constant speed in
a circle is directed towards the center of the circle.
2.4.2 Apply the expression for centripetal acceleration.
Practice Problem 1
 A test car moves at a constant speed around a circular track. If the car is 48.2m from the track’s center and
has a centripetal acceleration of 8.05 m/s2, what is the car’s tangential speed?
 What are you given? Needed?
Practice Problem 2
 The cylindrical tub of a washing machine has a radius of 34 cm. During the spin cycle, the wall of the tub
rotates with a tangential speed of 5.5 m/s. Calculate the centripetal acceleration of the clothes sitting against
the tub. What is given? needed?
 Classwork: (Holt: Physics) pg 236 Practice A
Centripetal Acceleration
 A bobsled travels at 34 m/s and goes around two turns in the track as seen here. What is the acceleration of
the sled in each turn?
2.4.3 Identify the force producing circular motion in various situations.
Centripetal Force
www.physicseh.com has some great resources. Use code to the right.
 Any force that causes an object to follow a circular path
 Watch the demo. (spinning cup of water)
 What provided the Centripetal Force on the cup?
 On the water?
 Do you know how your washing machine works?
 Centripetal force is necessary for _____________ motion.
 What would happen if the string attached to the cup broke?
 When driving in a circle, in what direction is a force acting on you?
 Pushing you outward from the circle, or inward?
 If you are swinging a yo-yo in a circle, and the string breaks…. What path does the yo – yo take??
 HOWEVER, People commonly think there is a force pushing you out from the circle
 Feels like you are being pushed outward
 Example ….. The Rotor- amusement park ride, a centrifuge, CD on your dashboard moving to the
right when your turning left
 Why is this??




The Rotor
So why is there no Force pushing you out from the circle??
A force does not cause this…… your _____________ does!!
Inertia makes you want to stay in a straight line, and by going in a circle, you are fighting your own inertia
 This is how Rotor works, and why CD on dashboard happens
 The only actual force acting on you is the Centripetal Force




Centripetal means “center- Seeking”
Force pushes you _____________ the center of the circle
Is the force that keeps you moving in a circle, and keeps your inertia from taking you in a straight line
Centripetal Force is affected by.. ________ (m), tangential speed (vt), and _____________ (r)
 Inertia wants to take objects in a _____________ line, to the circular path
 Inertia is why you feel like your being pushed outward
 This outward pushing is sometimes called the _____________ Force, but it is not actually a force, is
only inertia
 Every object that moves in circular motion must experience a centripetal force from somewhere




By definition – the __________ force that is directed toward the center of the circle.
This force is provided by a frame of reference
Consider a ladybug in a spinning can
The apparent centrifugal force on the lady bug is only an _____________ , not an interaction.
 _____________ Gravity - A spinning wheel can provide a “gravity” to occupants within it.
 If multiple rings are built, the gravity would vary depending on distance from center.
 Outer edge 1g, then ½ way is 0.5g
Centripetal Force
 The force equation will not change:
 However, remember this is now Fc, so…
Practice Problem 3
 A bicyclist is riding at a angular speed of 13.2m/s around a circular track. The magnitude of the centripetal
force is 377N, and the combined mass of the bicycle and rider is 86.5kg. What is the track’s radius?
 What are you given? needed?
Vertical Circular Motion
 If an object is suspened on the end of a cord and is rotated in vertical circle what forces are acting on it?
 Lets draw an FBD.
 At the top, we should see that the Fnet = Fc + Fg
OR
Ften = (mv2)/r + mg
 At the bottom
 We should see that the Fnet = Fc - Fg
OR
Ften = (mv2)/r - mg
Practice Problem 4
 A 0.5kg mass, suspended on the end of a light cord, 1.2m long, is rotated in a vertical circle at a constant
speed such that one revolution is completed in 0.4s. Calculate the tension in the cord when the weight is:
 A) at the top of the circle
 B) at the bottom of the circle
Velocity Practice
1. During their physics field trip to the amusement park, Tyler and Maria took a rider on the Whirligig. The
Whirligig ride consists of long swings which spin in a circle at relatively high speeds. As part of their
lab, Tyler and Maria estimate that the riders travel through a circle with a radius of 6.5 m and make one
turn every 5.8 seconds. Determine the speed of the riders on the Whirligig.
2. The tallest Ferris wheel in the world is located in Singapore. Standing 42 stories high and holding as
many as 780 passengers, the Ferris wheel has a diameter of 150 meters and takes approximately 30
minutes to make a full circle. Determine the speed of riders (in m/s and mi/hr) on the Singapore Flyer.
(GIVEN: 1.00 m/s= 2.24 mi/hr)
3. During the spin cycle of a washing machine, the clothes stick to the outer wall of the barrel as it spins at
a rate as high as 1800 revolutions per minute. The radius of the barrel is 26 cm.
a. Determine the speed of the clothes (in m/s) which are located on the wall of the spin barrel.
b.
Determine the acceleration of the clothes.
4. Elmira, New York boasts of having the fastest carousel ride in the world. The merry-go-round at
Eldridge Park takes riders on a spin at 18 mi/hr (8.0 m/s). The radius of the circle about which the
outside riders move is approximately 7.4 m.
a. Determine the time for outside riders to make one complete circle.
b. Determine the
acceleration of the riders.