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Rotation: circular motion around an inside axis - example the earth spinning on its own axis. Revolution: circular motion around an outside axis - example the earth moving around the sun. Circular motion • We have several ways to describe the speed at which an object turns • Tangential speed • Linear speed • Rotational speed • Angular velocity Circular motion Tangential velocity or VT which describes the speed at which an ant on the outside of the spinning turntable would be traveling at any instant relative to an outside observer. This is also known as linear velocity. This can also be thought of as the speed the ant would be going if he suddenly flew off of the rotating disk. Circular motion • Rotational velocity or (the greek lower case letter omega). • This is a measure of how fast an object is moving with relation to its axis of rotation. This motion will be described by how many revolutions the object makes around it axis of rotation. We will measure it in Revolutions per minute or RPMs in this class. Linear speed or velocity = tangential speed or velocity = distance/time and is measured in “meter/second” The red arrow represents the linear velocity rotational speed or velocity or angular speed or velocity, (omega), = = number of rotations time and is measured in RPM’s or degrees or radians second second Measure the time it takes for the blue arrow to go around once, its period,T, and calculate its angular speed in rotations per second. On a spinning turn table which point has the fastest speed? Well, it really depends! Which has the greatest vT? Which has the greatest ? To calculate the linear velocity we could take distance/time Or the circumference/time v = 2πr/T If the diameter of the circle is 4 m and the period is 3 seconds calculate the linear velocity. If something moves in curved path must there be a force on it? B A C v A ball is going around in a circle attached to a string. If the string breaks at the instant shown, which path will the ball follow? 10 Centripetal Force – A center-seeking force that causes an object to follow a circular path. Centripetal force Centripetal force Causes circular motion it is a real force “center seeking” What is the direction of the centripetal force? What direction would the acceleration be? G Force, 10 m/s/s or your weight • • • • • • • • • • • • • 0 stationary or moving at a constant velocity 0.4 "pedal to the metal" in a typical American car 1.7 "pedal to the metal" in a Formula One race car 2 Extreme Launch™ roller coaster at start 3 space shuttle, maximum at takeoff**; jet fighter landing on aircraft carrier 8 limit of sustained human tolerance 25 R. F. Gray, centrifuge*, 5 s duration, 40 USAF chimpanzee, centrifuge*, 60 s duration, 35 - 40J. P. Stapp, rocket powered impact sled, 1 s duration, 60 chest acceleration limit during car crash at 48 km/h with airbag 70 - 100 crash that killed Diana, Princess of Wales, 83 E. L. Beeding, rocket powered impact sled, 0.04 s duration, 247 USAF chimpanzee, rocket powered impact sled, 0.001 s duration, Centrifugal force “center-fleeing”, away from center Apparent outward force experienced by a rotating body Fictitious force – it is not real but do to the effect of inertia What is the direction of the centrifugal force? Centrifugal Force Rotational direction The whiteboard was being carried along a straight line path; the ball rest on top of the whiteboard and followed the same straight-line path. Then suddenly, the board was turned leftward to begin a circular motion; yet the ball kept moving straight. An accelerometer measures the acceleration. When the water in this accelerometer feels a lurch, a fictitious force, due to the effect of inertia When the accelerometer is accelerated uniformly in a straight line it will look like this When the accelerometer is rotated it will look like this Directions • • • • Linear velocity Angular acceleration Centripetal Force Centrifugal Force Formula’s = revolutions/time v = 2πr/T Fc = mv2/r A linebacker rides on the outside horse of a merry-go-round. The merry-goround’s diameter is 10 m it takes 5 seconds to complete 1 rotation. If the linebacker has a mass of 100 kg… Is he revolving or rotating? He is revolving….. The merry-go-round is rotating A linebacker rides on the outside horse of a merry-go-round. The merry-goround’s diameter is 10 m it takes 5 seconds to complete 1 rotation. If the linebacker has a mass of 100 kg… Calculate his linear velocity. 2r V T T 2 5m V T 6.28m / s 10 s of a merry-go-round. The merry-goround’s diameter is 10 m it takes 5 seconds to complete 1 rotation. If the linebacker has a mass of 100 kg… Calculate his centripetal force . 2 mv FC r 100kg(6.28m / s) 2 FC 5m kgm FC 789 2 or 789 Ninward s A linebacker rides on the outside horse of a merry-go-round. The merry-goround’s diameter is 10 m it takes 5 seconds to complete 1 rotation. If the linebacker has a mass of 100 kg… Calculate his centrifugal force. It’s not real, just like….. How does a train stay on the tracks? Believe it or not it is not the inner rim. The rail often does not touch it The wheels of the train are tapered. A cylinder rolls straight, whereas a cone will roll in a circle. Why? Which part of the tapered wheel moves with a greater VT? The part with the smaller radius A, or the larger radius B? Since B is moving faster it covers more distance and causes it turn. Let’s see what happens if we roll a cylinder wheel down a Curved track Will the wheel stay on the track? If the track starts turning right, underneath the train, (which has plenty of momentum), what will happen? There will be nothing to make the wheels turn right It does not correct itself as it slides off the track It is a train wreck Let’s see what happens if we roll a tapered wheel like the one shown down a track Will the wheel stay on the track, if the track starts turning left? The trains momentum tries to carry it straight forward. It does not correct itself, it wants to go right which is opposite of direction it needs to go! Faster Slower What happens if the track turns left The right wheel will move faster, with the same rotational speed but a larger VT, and the left wheel will move slower, so the train will roll to the left and self corrects. Staying on track. Faster Slower Slower Faster So if you want Thomas the Train to turn, you let its momentum do the work for you! If you want the train to turn left, you just make the tracks turn left and the rest happens by itself!! Horray for Thomas the Train! Slower Faster Trains are really smart, and very useful. But some are Evil! Artificial Gravity Space Station What would happen if the rotation was faster? What would happen if you increased the radius of the space station? To feel 1 g force, if the space station is larger would it have to be spinning as fast? Does an astronaut have to apply a force to an apple keep it moving in a circle? Would the astronaut feel “weight” from the apple? What would happen if he lets go of it? Is there a net force on it when he lets it go? What direction does the apple go as seen by the astronaut? Inertia - resists acceleration, a property of matter, a kind of laziness of matter depends on the mass Rotational Inertia “The moment of inertia” “I”, resists rotational acceleration, depends on the distribution of the mass, that is where the mass is located The further the mass is away from the axis of rotation, fulcrum, the greater the rotational inertia, that is the more lazy it to change its rotational motion. If these two rods have the same mass and CG but rod A has the mass located in the center and rod B has most of the mass located at the ends. Which is harder to rotate? Why? What happens when you put an equivalent force on each roll? Which one will rotate easier? Why? Which of these would have the least rotational inertia in their legs? Which would have the fastest gate? A solid hoop and a hollow cylinder roll down an incline. Which one will have the greatest rotational inertia? Why? Which one will be more sluggish? Which one will win the race? angular momentum (A.M.) is equal to - rotational velocity or - angular velocity, TIMES, I - rotational inertia or the moment of inertia A.M. = I conservation of angular momentum the total angular momentum of a system does NOT change, unless an outside force acts on it, therefore, angular momentum before = angular momentum after Ibefore = Iafter