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Chapter 6

Chapter 6. Circular Motion and Other Applications of Newton’s Laws of Motion. 6.1 2 nd Law and Uniform Circular Motion. Centripetal Force- A circular path, means centripetal acceleration A Force is REQUIRED to cause accel . The Σ F on the radial axis causes the centripetal acceleration

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Chapter 6

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  1. Chapter 6 Circular Motion and Other Applications of Newton’s Laws of Motion

  2. 6.1 2nd Law and Uniform Circular Motion • Centripetal Force- • A circular path, means centripetal acceleration • A Force is REQUIRED to cause accel. • The ΣF on the radial axis causes the centripetal acceleration (Forces that point in are +, out - )

  3. 6.1

  4. 6.1 Remember, the axis with acceleration points towards the axis of rotation (center of the circle) Quick Quizzes p. 152 Example Problems 6.2, 6.3, 6.4, 6.5, 6.6

  5. 6.1 Other Examples: G-Forces, What can you withstand? Water in the bucket, minimum ac to not fall out?

  6. 6.2 Nonuniform Circular Motion • If an object travels with varying speed in the circular path, it has both at and ar (ac) components. • It must also have similar radial and tangential force components. • ΣFr (points towards the center) • ΣFt (points tangent to path)

  7. 6.2 • Quick Quizzes p. 157 • Example 6.7

  8. 6.3 Motion in Accelerated Frames • Newton’s Laws of Motion are only valid in inertial frames (non accelerating). • In an accelerated frame (air hockey/train) there are apparent forces. • Fictitious Force • Forces that appear to exist but no 2nd interacting object can be located. • Examples…

  9. 6.3 • “Centrifugal Force” • Outward “force” when traveling in a curved or rotational path. (Fc is not large enough).

  10. 6.3 • “Coriolis Force” • “Force” that appears in rotating reference Frames,

  11. 6.3 • Fictitious forces are not real, but they do arise from measurable effects. Quick Quiz Pg 160 Examples 6.8, 6.9

  12. 6.4 Motion w/ Resistive Forces • Object moving though a fluid (gas/liquid) medium encounters resistance (Drag). • R- Resistive force generally depends on the speed of the object in complex ways. Two Approximations • R ~ v at slow speeds or small objects • R ~ v2 at high speeds or large objects

  13. 6.4 • R proportional to v • The resistive force R = -bv • Where v is the velocity and b is a constant that depends on the properties of the medium and dimensions of the object. • b has dimension MT-1 units kg/s.

  14. 6.4 • Object sphere falling through a liquid. • When v = 0 m/s, a = g (knew this already)

  15. 6.4 • a = 0 m/s2, when R = mg • This is called terminal velocity • Find vT

  16. 6.4 • To find v as a function of time requires DiffEq. • End Result • Time Constant (time to reach 63.2% of vT)

  17. 6.4 Example 6.10 p. 164

  18. 6.4 • R proportional to v2 • For objects moving at high speeds through the air the resistive force can be approximated as • Where ρ is the density of air • A is the cross-sectional area of the object • D is the drag coefficient (dimensionless) D ~ .5 for spherical shapes D can go up to ~ 2 for irregular shapes

  19. 6.4 • For a falling object at high speed… • To find vT , set a = 0 so…

  20. 6.4 • Quick Quiz p. 165 • Example 6.13

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