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Chapter 6 Angular Motion

. Objectives: After completing this module, you should be able to:. Define and apply concepts of angular displacement, velocity, and acceleration.Draw analogies relating rotational-motion parameters (?, ?, ?) to linear (x, v, a) and solve rotational problems.Write and apply relationships between l

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Chapter 6 Angular Motion

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    1. Chapter 6 – Angular Motion

    2. Objectives: After completing this module, you should be able to: Define and apply concepts of angular displacement, velocity, and acceleration. Draw analogies relating rotational-motion parameters (?, ?, ?) to linear (x, v, a) and solve rotational problems. Write and apply relationships between linear and angular parameters.

    3. Objectives: (Continued) Define moment of inertia and apply it for several regular objects in rotation. Apply the following concepts to rotation: 1. Rotational work, energy, and power 2. Rotational kinetic energy and momentum 3. Conservation of angular momentum

    4. Rotation: An Introduction For some to travel once around a circle, the distance formula is … 2pr The time to go once around is referred to as the Period (T) V = In a circle V =

    5. Rotational Displacement, ?

    6. Definition of the Radian

    7. Definition of the Radian

    8. Example 1: A rope is wrapped many times around a drum of radius 50 cm. How many revolutions of the drum are required to raise a bucket to a height of 20 m?

    9. Example 2: A bicycle tire has a radius of 25 cm. If the wheel makes 400 rev, how far will the bike have traveled?

    10. Angular Velocity

    11. Example 3: A rope is wrapped many times around a drum of radius 20 cm. What is the angular velocity of the drum if it lifts the bucket to 10 m in 5 s?

    12. Example 4: In the previous example, what is the frequency (rev/s) of revolution for the drum? Recall that w = 10.0 rad/s.

    13. Angular Velocity continued

    14. Linear Speed

    15. Angular and Linear Speed

    16. Examples:

    17. Angular Acceleration

    18. Angular Acceleration

    19. Acceleration Example

    20. Example 5: The block is lifted from rest until the angular velocity of the drum is 16 rad/s after a time of 4 s. What is the average angular acceleration?

    21. Angular and Linear Acceleration:

    23. 6.3 – Dynamics (Forces) and Circular Motion

    24. 6.3 – Dynamics (Forces) and Circular Motion

    25. 6.3 – Dynamics (Forces) and Circular Motion

    26. 6.4 – Apparent Forces during Circular Motion

    27. 6.5 – Orbits

    28. 6.5 – Orbits

    29. 6.5 – Orbits

    30. 6.5 – Orbits

    31. 6.5 – Orbits

    32. 6.5 – Orbits

    33. 6.6 – Newton’s Law of Gravity

    34. 6.6 – Newton’s Law of Gravity

    35. Linear Example: A car traveling initially at 20 m/s comes to a stop in a distance of 100 m. What was the acceleration?

    36. Angular analogy: A disk (R = 50 cm), rotating at 600 rev/min comes to a stop after making 50 rev. What is the acceleration?

    37. Problem Solving Strategy: Draw and label sketch of problem. Indicate + direction of rotation. List givens and state what is to be found.

    38. Example 6: A drum is rotating clockwise initially at 100 rpm and undergoes a constant counterclockwise acceleration of 3 rad/s2 for 2 s. What is the angular displacement?

    40. CONCLUSION: Chapter 11A Angular Motion

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