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Tutorial 13 Planar dynamics of rigid body

Tutorial 13 Planar dynamics of rigid body. Zhengjian, XU DEC 3rd, 2008. Rotation about a fixed axis for a mass point. Angular momentum:. Where H is the angular momentum with respect to the center of mass. Calculation of moment of inertia. A. O. B. A bar:. L. y. Rectangle:. h. O.

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Tutorial 13 Planar dynamics of rigid body

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  1. Tutorial 13 Planar dynamics of rigid body Zhengjian, XU DEC 3rd, 2008

  2. Rotation about a fixed axis for a mass point Angular momentum:

  3. Where H is the angular momentum with respect to the center of mass

  4. Calculation of moment of inertia A O B A bar: L y Rectangle: h O x b y Circle: R x O

  5. Another method: parallel-axis method

  6. Example 1 • A horizontal force F = 30 lb is applied to the 230-lb refrigerator as shown. Friction is negligible. • (a) What is the magnitude of the refrigerator’s acceleration? • (b) What normal forces are exerted on the refrigerator by the floor at A and B?

  7. Solution: • Assume the box doesnot tip over, then the box has only horizontal velocity and acceleration. F Force equilibrium: O Vx, ax 60in G 28in NA NB 28in What’s the condition of F for tipping?

  8. Example 2 • Bar AB rotates with a constant angular velocity of 10 rad/s in the counterclockwise direction. The masses of the slender bars BC and CDE are 2 kg and 3.6 kg, respectively. The y axis points upward. • Determine the components of the forces exerted on bar BC by the pins at B and C at the instant shown.

  9. By 1. Dynamics analysis: Bx B Cy G C Cx Moment equlibrium equations D Cx C E Cy

  10. 2 Kinematics analysis By VB Bx VC B D Cx C E Cy C Cy Cx At this instant, point A is the instantaneous center of BC. From AB-BC: From CD:

  11. From the kinematics analysis:

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