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Rotation of a Rigid Object About a Fixed Axis 10 5/25/20151 Hamid

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Presentation on theme: "Rotation of a Rigid Object About a Fixed Axis 10 5/25/20151 Hamid"— Presentation transcript:

1 Rotation of a Rigid Object About a Fixed Axis 10 5/25/20151 Hamid Salvdari*salvdari@yahoo.com*salvdari.blogfa.com

2 10.1 Angular Displacement, Velocity, and Acceleration10.2 Rotational Kinematics: Rotational Motion with Constant Angular Acceleration10.3 Angular and Linear Quantities10.4 Rotational Energy10.5 Calculation of Moments of Inertia10.6 Torque10.7 Relationship Between Torque and Angular Acceleration10.8 Work, Power, and Energy in Rotational Motion 5/25/20152 Hamid Salvdari-salvdari@yahoo.com- salvdari.blogfa.com

3 A rigid object is one that is nondeformable—that is, it is an object in which the separations between all pairs of particles remain constant. In this chapter, we treat the rotation of a rigid object about a fixed axis, which is commonly referred to as pure rotational motion. 5/25/20153 Hamid Salvdari-salvdari@yahoo.com- salvdari.blogfa.com

4 10.1 Angular Displacement, Velocity, and Acceleration one radian is the angle subtended by an arc length equal to the radius of the arc. 5/25/20154 Hamid Salvdari-salvdari@yahoo.com- salvdari.blogfa.com

5 5/25/20155 Hamid Salvdari-salvdari@yahoo.com- salvdari.blogfa.com

6 10.1 Angular Displacement, Velocity, and Acceleration When rotating about a fixed axis, every particle on a rigid object rotates through the same angle and has the same angular speed and the same angular acceleration. 5/25/20156 Hamid Salvdari-salvdari@yahoo.com- salvdari.blogfa.com

7 10.2 Rotational Kinematics: Rotational Motion with Constant Angular Acceleration 5/25/20157 Hamid Salvdari-salvdari@yahoo.com- salvdari.blogfa.com

8 EXAMPLE : Rotating Wheel 5/25/20158 Hamid Salvdari-salvdari@yahoo.com- salvdari.blogfa.com

9 Solution 5/25/20159 Hamid Salvdari-salvdari@yahoo.com- salvdari.blogfa.com

10 10.2 Rotational Kinematics: Rotational Motion with Constant Angular Acceleration 5/25/201510 Hamid Salvdari-salvdari@yahoo.com- salvdari.blogfa.com

11 5/25/201511 Hamid Salvdari-salvdari@yahoo.com- salvdari.blogfa.com

12 5/25/201512 Hamid Salvdari-salvdari@yahoo.com- salvdari.blogfa.com

13 EXAMPLE : CD Player 5/25/201513 Hamid Salvdari-salvdari@yahoo.com- salvdari.blogfa.com

14 Solution 5/25/201514 Hamid Salvdari-salvdari@yahoo.com- salvdari.blogfa.com

15 Solution 5/25/201515 Hamid Salvdari-salvdari@yahoo.com- salvdari.blogfa.com

16 10.4 Rotational Energy 5/25/201516 Hamid Salvdari-salvdari@yahoo.com- salvdari.blogfa.com

17 EXAMPLE : The Oxygen Molecule 5/25/201517 Hamid Salvdari-salvdari@yahoo.com- salvdari.blogfa.com

18 Solution 5/25/201518 Hamid Salvdari-salvdari@yahoo.com- salvdari.blogfa.com

19 EXAMPLE : Four Rotating Masses 5/25/201519 Hamid Salvdari-salvdari@yahoo.com- salvdari.blogfa.com

20 Solution 5/25/201520 Hamid Salvdari-salvdari@yahoo.com- salvdari.blogfa.com

21 10.5 Calculation of Moments of Inertia 5/25/201521 Hamid Salvdari-salvdari@yahoo.com- salvdari.blogfa.com

22 EXAMPLE : Uniform Hoop 5/25/201522 Hamid Salvdari-salvdari@yahoo.com- salvdari.blogfa.com

23 Solution 5/25/201523 Hamid Salvdari-salvdari@yahoo.com- salvdari.blogfa.com

24 EXAMPLE : Uniform Rigid Rod 5/25/201524 Hamid Salvdari-salvdari@yahoo.com- salvdari.blogfa.com

25 Solution 5/25/201525 Hamid Salvdari-salvdari@yahoo.com- salvdari.blogfa.com

26 EXAMPLE : Uniform Solid Cylinder 5/25/201526 Hamid Salvdari-salvdari@yahoo.com- salvdari.blogfa.com

27 Solution 5/25/201527 Hamid Salvdari-salvdari@yahoo.com- salvdari.blogfa.com

28 5/25/201528 Hamid Salvdari-salvdari@yahoo.com- salvdari.blogfa.com

29 5/25/201529 Hamid Salvdari-salvdari@yahoo.com- salvdari.blogfa.com

30 5/25/201530 Hamid Salvdari-salvdari@yahoo.com- salvdari.blogfa.com

31 10.6 Torque The tendency of a force to rotate an object about some axis is measured by a vector quantity called torque (tau). 5/25/201531 Hamid Salvdari-salvdari@yahoo.com- salvdari.blogfa.com

32 EXAMPLE : The Net Torque on a Cylinder 5/25/201532 Hamid Salvdari-salvdari@yahoo.com- salvdari.blogfa.com

33 Solution 5/25/201533 Hamid Salvdari-salvdari@yahoo.com- salvdari.blogfa.com

34 10.7 Relationship Between Torque and Angular Acceleration 5/25/201534

35 Although each point on a rigid object rotating about a fixed axis may not experience the same – force, – linear acceleration, – linear speed, each point experiences the same angular acceleration angular speed at any instant. Therefore, at any instant the rotating rigid object as a whole is characterized by specific values for o angular acceleration, o net torque, o angular speed. 5/25/201535 Hamid Salvdari-salvdari@yahoo.com- salvdari.blogfa.com

36 EXAMPLE :Rotating Rod 5/25/201536 Hamid Salvdari-salvdari@yahoo.com- salvdari.blogfa.com

37 Solution 5/25/201537

38 CONCEPTUAL EXAMPLE 5/25/201538 Hamid Salvdari-salvdari@yahoo.com- salvdari.blogfa.com

39 EXAMPLE : Angular Acceleration of a Wheel 5/25/201539

40 Solution 5/25/201540

41 EXAMPLE : Atwood’s Machine Revisited 5/25/201541 Hamid Salvdari-salvdari@yahoo.com- salvdari.blogfa.com

42 Solution 5/25/201542 Hamid Salvdari-salvdari@yahoo.com- salvdari.blogfa.com

43 5/25/201543 Hamid Salvdari-salvdari@yahoo.com- salvdari.blogfa.com

44 10.8 Work, Power, and Energy in Rotational Motion 5/25/201544 Hamid Salvdari-salvdari@yahoo.com- salvdari.blogfa.com the radial component of F does no work because it is perpendicular to the displacement.

45 EXAMPLE : Rotating Rod Revisited 5/25/201545 Hamid Salvdari-salvdari@yahoo.com- salvdari.blogfa.com

46 Solution 5/25/2015 Hamid Salvdari-salvdari@yahoo.com- salvdari.blogfa.com 46

47 EXAMPLE : Connected Cylinders 5/25/2015 Hamid Salvdari-salvdari@yahoo.com- salvdari.blogfa.com 47

48 Solution 5/25/201548

49 5/25/2015 Hamid Salvdari-salvdari@yahoo.com-salvdari.blogfa.com 49

50 5/25/2015 Hamid Salvdari-salvdari@yahoo.com- salvdari.blogfa.com 50

51 5/25/2015 Hamid Salvdari-salvdari@yahoo.com- salvdari.blogfa.com 51

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