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Uniform Circular Motion

Uniform Circular Motion. What is uniform circular motion?. 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.

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Uniform Circular Motion

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  1. Uniform Circular Motion

  2. What is uniform circular motion? • 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

  3. Period and Speed • Often easier to use period T= time to complete 1 revolution instead of linear speed • Circle=2r • So if v=d/t then V= 2r/T REMEMBER: speed may be constant but velocity is not! Acceleration changes the direction.

  4. Vectors in circular motion • Velocity points tangent to circle • Acceleration points in to axis of rotation because a=v/ t and v is always towards center

  5. 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

  6. What provides Fc?

  7. DRAW Free body diagrams • 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!

  8. 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

  9. 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?

  10. 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? If net force is straight down, why doesn’t the car fall off the track?

  11. Banked Curves • Draw a free body diagram for a car traveling around a banked curve- even without friction Nsin is component of force keeping car on curve- even without any friction.

  12. Circular motion and universal gravitation • Satellites, planets, moons, etc can travel in circular paths- to solve, equate Fc to gravitational force

  13. 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

  14. 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 =42/GM Where T is period, M is mass of sun, R is radius of circular orbit (even though it’s not quite circular)

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