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Uniform Circular Motion

Uniform Circular Motion. Textbook: Chapter 5. Uniform Circular Motion. UCM is the motion at a constant (uniform) speed on a circular path. Is velocity constant in UCM ? No, because direction is changing Is acceleration constant in UCM ?

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Uniform Circular Motion

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  1. Uniform Circular Motion Textbook: Chapter 5

  2. Uniform Circular Motion • UCM is the motion at a constant (uniform) speed on a circular path. • Is velocity constant in UCM? • No, because direction is changing • Is acceleration constant in UCM? • Yes, because direction is constantly changing towards the center of the circle.

  3. UCM: Period • The period, denoted by T, is the time it takes an object to make one revolution in UCM. • The unit for period is _________ • The distance traveled over time T is the circumference of a circle. • The equation for circumference of a circle:

  4. UCM: Frequency • Frequency is how often an object makes a rotation. • Measured in # of cycles/second, or • 1/s which is known as Hertz, Hz • Abbreviated f • f = 1/T and T = 1/f

  5. UCM: Linear Speed • If you know the distance and the time, what is the equation for speed, v, during UCM? • v = 2r/T • v = 2rf

  6. Angular and Linear Speed Imagine an object rotating at a constant speed A and B are points on the object B A

  7. Angular and Linear Speed • Both points go one rotation in the same amount of time… But which one travels a greater linear distance? B A And, therefore, has a greater speed?

  8. v v1 v2 v2 R v1 s Centripetal Acceleration v1 and v2 are velocity vectors – same magnitude, different directions Δv is the vector you have to add to v1 to get v2

  9. Similar triangles: v2 R v1 s Centripetal Acceleration Dv = Ds v R But s = v t for smallt Dv = vDt v R Dv = v2 Dt R Rearranging… v v1 v2

  10. Centripetal Acceleration Try thisapplet.

  11. UCM: Acceleration • What is the direction of the acceleration vector during UCM? • Towards the center of the circle. • Centripetal = “Center-seeking” • Magnitude is given by the equation: ac = v2/r

  12. UCM: Force • Newton’s 2nd Law will tell us the centripetal force for UCM • What is the second law? • F = ma • So, magnitude of centripetal force is given by: • Fc= mac = mv2/r • What is the direction of Fc? • Towards the center of the circle

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