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## Circular Motion

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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**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. • 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**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. • 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**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.**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 Full spin. • Faster rotational speed, Star or smiley?? • Both the same, b/c entire record is rotating at the same rate**Are some of us moving with a greater LINEAR SPEED than**others?? • Yes, 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?? • No, 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 = ? v = 2πr/T**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 “Tangential Speed” v = 2πr/T**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? It takes 2 seconds to make one complete rotation.**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, CAN the cars still have an acceleration?**2.4.2Apply the expression for centripetal 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.**2.4.2 Apply the expression for centripetal acceleration.**• 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 center of the circle. ac = v2/r**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**ac = vt2/r • 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? • Vt = 19.7 m/s**Practice Problem 2**ac = vt2/r • 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? • A = 89 m/s2**Velocity Practice From Packet**• Classwork: (Holt: Physics) pg236 Practice A**Velocity Practice From Packet**• 7 m/s • 0.26 m/s • 49 m/s**Practice A Centripetal Acceleration**• 2.5m/s • 11m/s • 1.5m/s2 • 58.4m**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? Turn 1: 35 m/s2 Turn 2: 48 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?**2.4.3 Identify the force producing circular motion in**various situations. • Centripetal force is necessary for circular motion. • What would happen if the string attached to the cup broke?**2.4.3 Identify the force producing circular motion in**various situations. ? • 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**2.4.3 Identify the force producing circular motion in**various situations. • 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??**People Stand with backs against wall of a large cylinder,**cylinder then starts spinning, and people are seemingly pushed against the wall, then floor drops, and people are stuck against the wall. http://www.youtube.com/watch?v=uz_DkRs92pM The Rotor**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**2.4.3 Identify the force producing circular motion in**various situations. • Centripetal 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 Centripetal Force is affected by.. Mass (m), linear speed (vt), and radius (r)**Centripetal Force**• 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 B pg 238**1) 29.6kg 2) 40m 3) 40N 4) 35m/s**Can you identify the different sources of centripital force?**Watch Video**2.4.3 Identify the force producing circular motion in**various situations. • By definition – the net 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 effect, not an interaction.**Simulated 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… F = ma Fc = mac or Fc = mv2/r**Practice Problem 3**Fc = mv2/r • 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? • r = 40m**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 watch Video #2 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**Answer:**A) 143N B) 153N**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? Turn 1: 35 m/s2 Turn 2: 48 m/s2**TOPIC 6.1: Gravitational Fields and Forces**These notes were typed in association with Physics for use with the IB Diploma Programme by Michael Dickinson**What is gravity?**Is there gravity in space? Why do astronauts float? What keeps the moon from flying off in space?**6.1 Gravitational Force and Field**6.1.1 State Newton’s universal law of gravitation. Watch Veritesium Videos 1, 2, 3 http://www.youtube.com/watch?v=mezkHBPLZ4A&list=PL772556F1EFC4D01C http://www.youtube.com/watch?v=zN6kCa6xi9k&list=PL772556F1EFC4D01C http://www.youtube.com/watch?v=iQOHRKKNNLQ&list=PL772556F1EFC4D01C**Two cars are parked 3m away from each other. One car has a**mass of 1500kg while the other has a mass of 2000kg. What is the gravitational force between them?**6.1 Gravitational Force and Field**6.1.1 State Newton’s universal law of gravitation. • Galileo (1564-1642) – g = 9.81m/s2, even with different masses. • David Scott – feather and hammer dropped on the moon, Apollo 15 • Isaac Newton(1643-1727) – • Idea about a cannon ball that never hit the ground. • Orbit period of the moon – 27.3days • Radius of moons orbit – RM = 3.844 x 108m, RE = 6.378 x 106m • mid-1600s Earth’s and Moon’s masses had been determined • MM = 7.35 x 1022kg • ME = 5.98 x 1024kg)