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Chapter 10

Chapter 10. Rotational Motion (kinetic energy and moment of inertia). Radian Vs Degree. Using Radian. Example. Example. What is θ in radians and in degrees?. Angular velocity. v and ω. The dot goes around the circle of radius r=2m once every 10s . What is its v and ω ?.

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Chapter 10

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  1. Chapter 10 Rotational Motion (kinetic energy and moment of inertia)

  2. Radian Vs Degree

  3. Using Radian

  4. Example

  5. Example What is θ in radians and in degrees?

  6. Angular velocity

  7. v and ω The dot goes around the circle of radius r=2m once every 10s. What is its v and ω?

  8. Meaning of different variables

  9. Period T and frequency f

  10. Must remember this: Using this you can convert freely among ω, T, f and v.

  11. Example Given r =2m, T=10s, find v and ω.

  12. Example Given r =2m, f = 20rpm, find v and ω.

  13. Example A car takes 5 minutes to complete one circle on the race track. What is its angular velocity?

  14. y v (x,y) r x Equations of Circular Motion(Must Memorize)

  15. Units

  16. Angular acceleration α

  17. Equations of Motion Linear Circular

  18. Example: Wheel Radius r =2m Angular acceleration: α=3 rad/s2 Initial angular velocity ω0=0 rad/s After 5s, what is the final angular velocity? What angle has the wheel rotated. How far has the wheel rolled on the ground?

  19. Example A cyclist traveling at 5m/s accelerates up to 10m/s in 2s. Each tire has r =0.35m. A small pebble is stuck on the tire. What is the linear acceleration of the bike? What is the angular acceleration of the pebble?

  20. Example (Cont.) A cyclist traveling at 5m/s accelerates up to 10m/s in 2s. Each tire has r =0.35m. A small pebble is stuck on the tire. (c) What is the initial angular velocity?

  21. Example (Cont.) A cyclist traveling at 5m/s accelerates up to 10m/s in 2s. Each tire has r =0.35m. A small pebble is stuck on the tire. (d) Through what angle does the pebble revolve? (e) How far around the wheel has the pebble traveled?

  22. m1 m2 m3 2m 1m 5m Moment of Inertia r is the distance from the axis of rotation.

  23. Dependence on axis of rotation The moment of inertia will depends on the axis of rotation.

  24. Example 1 To find I, ask yourself: What is the distance r of each mass from the axis of rotation?

  25. Example 2 To find I, ask yourself: What is the distance r of each mass from the axis of rotation?

  26. I for extended objects

  27. Rotational Energy

  28. Example

  29. A sphere rolling down from rest. Find velocity at the bottom. Example

  30. Example

  31. What is the sphere slides down instead? Example (modified)

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