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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