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Transcript
Uniform Circular Motion QuickTime™ and a decompressor are needed to see this picture. What is uniform circular motion? QuickTime™ and a decompressor are needed to see this picture. • Constant speed • Circular path • Must be an unbalanced force acting towards axis of rotation- think free body diagrams! • Ex of forces: tension, banked curves, gravitation Period and Speed QuickTime™ and a decompressor are needed to see this picture. • Often easier to use period T= time to complete 1 revolution instead of linear speed • Circle=2r • So if v=d/t then V= 2r/T REMEMBER: speed may be constant but velocity is not! Acceleration changes the direction. Vectors in circular motion QuickTime™ and a decompressor are needed to see this picture. • Velocity points tangent to circle • Acceleration points in to axis of rotation because a=v/ t and v is always towards center Centripetal Acceleration and Force • ac=v2/r and points in • Fc=macdue to Newton’s 2nd law • Sometimes written by replacing a so: Fc=mv2/r QuickTime™ and a decompressor are needed to see this picture. What provides Fc? QuickTime™ and a decompressor are needed to see this picture. QuickTime™ and a decompressor are needed to see this picture. QuickTime™ and a decompressor are needed to see this picture. QuickTime™ and a decompressor are needed to see this picture. DRAW Free body diagrams • QuickTime™ and a decompressor are needed to see this picture. • Ex: An athlete who weights 800N is running around a curve at a speed of 5.0m/s in an arc whose radius is 5.0m. What provides the centripetal force? • Draw a free body diagram! FRICTION! Now solve… • What is the centripetal force? • What would happen if the radius of the curve were smaller? • Fc=mv2/r • Mass=Fw/g Fc=400N QuickTime™ and a decompressor are needed to see this picture. Now take it 2 step further… • If the coefficient of static friction btwn the shoe and the track =1 then will the runner slip? • How does changing the radius of the curve affect whether the runner will slip? Another example • A roller coaster enter as loop. At the very top the speed of the car is 25m/s and the acceleration points straight down. If the diameter of the loop is 50m and the total mass of the car=1200kg, what is the magnitude of the normal force? • Start with a free body diagram- what forces are acting? QuickTime™ and a decompressor are needed to see this picture. If net force is straight down, why doesn’t the car fall off the track? Banked Curves QuickTime™ and a decompressor are needed to see this picture. Nsin is component of force keeping car on curve- even without any friction. • Draw a free body diagram for a car traveling around a banked curve- even without friction Circular motion and universal gravitation • Satellites, planets, moons, etc can travel in circular paths- to solve, equate Fc to gravitational force QuickTime™ and a decompressor are needed to see this picture. Kepler’s Laws: 1 and 2 • Every planet moves in elliptical orbit with sun at 1 focus • As planet moves in its orbit, a line drawn from sun to planet sweeps out equal area in equal time QuickTime™ and a decompressor are needed to see this picture. QuickTime™ and a decompressor are needed to see this picture. Kepler’s 3rd Law • Remember Newton’s Universal Gravitation, G? • Kepler equated the force of G with the laws of circular motion to get: T2/R3 is a constant =42/GM Where T is period, M is mass of sun, R is radius of circular orbit (even though it’s not quite circular)