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. 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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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