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Chap. 7 Dynamics III: Motion in a Circle

Chap. 7 Dynamics III: Motion in a Circle. 7.1 Uniform Circular Motion 7.2 Velocity and Acceleration in Uniform Circular Motion 7.3 Dynamics of Uniform Circular Motion 7.4* Circular Orbital 7.6 Nonuniform Circular Motion.

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Chap. 7 Dynamics III: Motion in a Circle

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  1. Chap. 7 Dynamics III:Motion in a Circle 7.1 Uniform Circular Motion 7.2 Velocity and Acceleration in Uniform Circular Motion 7.3 Dynamics of Uniform Circular Motion 7.4* Circular Orbital 7.6 Nonuniform Circular Motion

  2. Stop to think 7.1 P 181Stop to think 7.2 P 185Stop to think 7.3 P 190Stop to think 7.4 P 196 • Example 7.3 P 181 • Example 7.5 P 186 • Example 7.6 P 187 • Example 7.7 P 188 • Example 7.10 P 199

  3. Uniform Circular Motion • Period • Angular Position

  4. Angular Velocity • Average angular velocity =∆θ/∆t • Instantaneous angular velocity • The angular velocity is constant during uniform circular motion

  5. An old-fashioned single-play vinyl record rotates 30.0 rpm . What are (a) the angular velocity in rad/s and (b) the period of the motion? • rpm: revolution per minute. 1 rpm = 2π/60 (rad)/s

  6. Velocity and acceleration in uniform circular motion

  7. Velocity in uniform circular motion The magnitude of velocity is a constant V =r dθ/dt=ωr Has only a tangential Component

  8. Centripetal acceleration

  9. The magnitude of centripetal acceleration P184 Towards center of circle

  10. Dynamics of Uniform Circular Motiion • From the Newton’s second law, a particle of mass m moving at constant speed V around a circle of radius r must have a net force of magnitude (mV2/r) pointing toward the center of the circle

  11. The Conical Pendulum • A small object of mass m is suspended from a string of length L. how many forces act on the object when it revolved with constant speed V in a horizontal circle?

  12. Turning the corner

  13. Circular Orbits The real weight force is always directed Toward the center of the planet downwards

  14. Nonuniform circular motion

  15. Tangential acceleration Change the speed Here α is angular acceleration

  16. Dynamics of nonuniform circular motion The radial force causes the Centripetal acceleration. It makes Velocity change direction. The tangential force causes The tangential acceleration. It Makes speed change

  17. Ex. P.47 Passenger stand inside a 16-m-diamete rotation ring.After the ring has acquired sufficient speed, It tilts into a vertical plane, as shown in the Figure At the top: At the bottom:

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