Download Circular Motion

Circular Motion
Definition: Uniform Circular motion is the motion of an object traveling at a constant (uniform) speed on a
circular path
 Axis – 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
How do we describe how fast something is rotating??
 Speeds for objects in a straight line are called linear (or tangential) 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 linear 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 --- RPM’s
 Below, a record spinning on a axis through its center (black dot)
 Faster linear speed, Star or Smiley??
 Smiley, travels a greater distance for each
 Faster rotational speed, Star or smiley??
 Both the same, b/c entire record is rotating at the same rate
 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 = ?
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 car still has an acceleration.
 This is due to what defines acceleration: 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 = (angular speed)2 / radius of circular path
 The acceleration is still a vector qty, and will always point toward the center of the circle.
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?
 Answer:19.7m/s
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.
 Answer = 89 m/s2
Centripetal Force
 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 circular 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??
 Ans. -- Inwards, toward the center of the circle
 Ans -- yo- yo goes in a path tangent to the circle
 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??
 So why is there no Force pushing you out from the circle??
 A force does not cause this…… your INERTIA 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 - means “center- Seeking”
 Force pushes you toward 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
 Inertia wants to take objects in a tangent line, to the circular path
 Inertia is why you feel like your being pushed outward
 This outward pushing is sometimes called the Centrifugal 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
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?
 Answer: 40m
Vertical Circular Motion
 If an object is suspended on the end of a cord and is rotated in vertical circle what forces are acting on it?
 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
 Answer: A) 143N B) 153N