人教版英语八年级下Unit9课件5.ppt

Circular motionHave you ever been to an amusement park?Fig. 05.19Why somebody needs to know about circular motionvOtherwise we wouldn’t go on those rides?vSpace station , satellites, live from overseasvPlanets, Comets and MoonsUniform Circular MotionvVelocity is a vector, it has both direction and magnitudevSimplest case: direction constant, magnitude changes. Linear MotionvWe will now study another “simple” case: magnitude is constant and direction continually changes. vUniform Circular Motion8Circular MotionX θ = 0yifHow do we locate something on a circle?Give its angular position θWhat is the location of900 or π/29Circular Motion is the angular position.Angular displacement:Note: angles measured Clockwise (CW) are negative and angles measured (CCW) are positive.  is measured in radians.2 radians = 360 = 1 revolutionxyifWhat is a radian?vC =2πr = (total angle of one rotation) x rvRadian measure relates displacement along circumference to angular displacement11Circular MotionX θ = 0yifHow do we locate something on a circle?Give its angular position θWhat is the location of900 or π/2From θ =0 to θ = 900 we have gone ¼ of way around ¼ of 2π =π/212xyifrarclength = s = r is a ratio of two lengths; it is a dimensionless ratio! This is a radian measure of angleIf we go all the way round s =2πr and Δθ =2 πQuestion vA child runs around the circular ledge of a fountain which has a diameter of 6.5 m. After the child has run 9.8 m, her angular displacement is A) 0.48 rad. B) 6.0 rad. C)1.5 rad. D)3.0 rad.14If we move around a circle we change θ. How fast does θ change?The average and instantaneous angular velocities ω are: is measured in rads/sec.v and ωvFor circular motion—How far do you travel during Δt if you are spinning at an angular velocity ω?v How far? s = Δθ r = ω Δt rvHow fast? (speed)vv = s/Δt =ωrv =ωrQuestion vA child runs around the circular ledge of a fountain which has a diameter of 6.5 m. If it takes her 72 seconds to run all the way around, her angular velocity isvA)0.087 rad/svB)0.57 m/svC)0.17 rad/svD)0.044 rad/sQuestion vA CD makes one complete revolution every tenth of a second. The angular velocity of point 4 is:vA)the same as for pt 1.vB)twice that of pt 2.vC)half that of pt 2.vD)1/4 that of pt 1.vE)four times that of pt 1.Question vA CD makes one complete revolution every tenth of a second. Which has the largest linear (tangential) velocity?vA)point 1vB)point 2vC)point 3vD)point 419The time it takes to go one time around a closed path is called the period (T).Comparing to v = r:ω = v/rf is called the frequency, the number of revolutions (or cycles) per second. f = 1/T20 Centripetal AccelerationHere, v  0. The direction of v is changing. If v  0, then a  0. The net force cannot be zero. Consider an object moving in a circular path of radius r at constant speed.xyvvvv21Conclusion: to move in a circular path, an object must have a nonzero net force acting on it.It is always true that F = ma. What acceleration do we use?22The velocity of a particle is tangent to its path. For an object moving in uniform circular motion, the acceleration is radially inward.23All three angles =Δθ = Δr/r =vΔt/rΔv=vΔθ = v2 Δt/r24The magnitude of the radial acceleration is:Δv=vΔθ = v2 Δt/rar = Δv/Δt = v2Δt/rΔtWhat makes it go round?A particle in circular motion is accelerating sothere must be a force providing this accelerationv F =ma v = mv2/rQuestion A spider is sitting on a turntable that is rotating at 33rpm. The acceleration a of the spider isv A) greater the closer the spider is to the central axis.v B) greater the farther the spider is from the central axis.v C) nonzero and independent of his location.v D) zero.28Example (text problem 5.12): The rotor is an amusement park ride where people stand against the inside of a cylinder. Once the cylinder is spinning fast enough, the floor drops out.(a) What force keeps the people from falling out the bottom of the cylinder?Draw an FBD for a person with their back to the wall:xywNfsIt is the force of static friction.29Example (text problem 5.12): The rotor is an amusement park ride where people stand against the inside of a cylinder. Once the cylinder is spinning fast enough, the floor drops out.(a) What force keeps the people from falling out the bottom of the cylinder?xywNfs(b) If s = 0.40 and the cylinder has r = 2.5 m, what is the minimum angular speed of the cylinder so that the people don’t fall out?30Example (text problem 5.79): A coin is placed on a record that is rotating at 33.3 rpm. If s = 0.1, how far from the center of the record can the coin be placed without having it slip off?Apply Newton’s 2nd Law:xywNfsDraw an FBD for the coin:CentrifugevSalad spinners, spin drying , Uranium centrifugesvNeed force to keep spinning. If object overcomes that force it moves out of circle.(spinners, drying)vMore massive particles are harder to rotatevFr = Mv2/r (uranium)vIf there is no normal force or friction (which depend on M) more massive particles will be “thrown” out of circle.Question vAn object is in uniform circular motion. Which of the following statements is true?vA)Velocity = constantvB)Speed = constantvC)Acceleration = constantv D) Both B and C are trueFig. 05.12Fig. 05.1336 Unbanked and Banked CurvesExample (text problem 5.20): A highway curve has a radius of 825 m. At what angle should the road be banked so that a car traveling at 26.8 m/s has no tendency to skid sideways on the road? (Hint: No tendency to skid means the frictional force is zero.)Take the car’s motion to be into the page.37Nonuniform Circular MotionHere, the speed is not constant.There is now an acceleration tangent to the path of the particle.The net acceleration of the body is atvaraRecall v is tangential =ωr38ataraat changes the magnitude of v.ar changes the direction of v.Can write:Fig. 05.1940Example: What is the minimum speed for the car so that it maintains contact with the loop when it is in the pictured position?FBD for the car at the top of the loop:NwyxApply Newton’s 2nd Law:r41The apparent weight at the top of loop is:N = 0 whenThis is the minimum speed needed to make it around the loop.Example continued:•A boy swings on a tire swing. When is the tension in the rope the greatest?•A)At the highest point of the swing.•B)Midway between his highest • and lowest points.•C)At the lowest point in the swing.•D)It is constant.43 Tangential and Angular AccelerationThe average and instantaneous angular acceleration are: is measured in rads/sec2.44Recall that the tangential velocity is vt = r. This means the tangential acceleration is 45The kinematic equations:LinearAngularWithv r=67.5mv T=30 minv tto cruise =20sv α = ?v Δθ =?Gravity and Circular MotionvWhat keeps the Moon going around the Earth? Why do planets go around the Sun? What determines the orbits of satellites?vHow can we “weigh” the Earth? the Sun?vWhat is the Universe made of?Circular OrbitsConsider an object of mass m in a circular orbit about the Earth.EarthrThe only force on the satellite is the force of gravity:The speed of the satellite:How much does the Earth weigh?Solve for MeWe measure v of satellite , we measure how high it is (r) , we can measure G in the lab, hence we calculate Me .We have weighed the Earth!Weigh the SunvWhat about the Earth going around the sun?vGravity keeps the Earth moving around Sun. Same equations as for the satellite. Gravity is universalvr R (distance from Sun to Earth)vms MsWeighing the SunvHow fast are we traveling around the Sun? (v)vv=2πR/T T = 1 yearvFrom astronomy we can measure RvWe have weighed the SunGravitational OrbitsvWe can do this for any objects in gravitational orbit around each other. Independent of the mass of the orbiting object. Depends only on the mass of the central object. vPlanets around Sun, Moons around Planets …..vGeneral formulaWhat is the Universe made of ?What is the Universe made of ?vWe see mostly galaxies. vWe can measure the velocity of stars in a galaxyvMost of the bright stuff (luminous matter, stars) is in the center. We are made of the same stuff as stars.vWe expect57Example: How high above the surface of the Earth does a satellite need to be so that it has an orbit period of 24 hours?From previous problem:Also need,Combine and solve for r:58Example: How high above the surface of the Earth does a satellite need to be so that it has an orbit period of 24 hours?From previous slide:Also need,Combine these expressions and solve for r:。