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Chapter 7 Plane Kinetics of Rigid Body

Chapter 7 Plane Kinetics of Rigid Body. y. x. Moment of inertia of a rigid body about an axis. I G is the moment of inertia about G. Example : Moment of inertia of a cylinder about the axis. r. L. d r. a. Parallel axis theorem :. I o = I G + mh 2. Example.

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Chapter 7 Plane Kinetics of Rigid Body

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  1. Chapter 7 Plane Kinetics of Rigid Body

  2. y x Moment of inertia of a rigid body about an axis. IG is the moment of inertia about G.

  3. Example : Moment of inertia of a cylinder about the axis. r L dr a

  4. Parallel axis theorem : Io = IG + mh2

  5. Example a h 5

  6. For a thin plate, the moment of inertia about the z-axis is : z y x y Iz = Ix + Iy x

  7. Radius of gyration is defined as: Rg = (IG /m)1/2 Example: Radius of gyration of a circular disc. a

  8. Self-learning exercise b dx b dx

  9. Angular momentum Assuming that the acceleration of Q = 0, hence

  10. 0.1m Cut 0.3m 0.3m Example: Find T1 , T2 and aG when BF is cut. At the moment when the string at B is cut, vA = 0 3 equations v.s. 3 unknowns 0.3m

  11. Example A compound wheel has an inner wheel with a radius rin=150 mm and an outer wheel of radius rout = 450 mm. Radius of gyration about G is Rg= 0.25m. If m = 70 kg, s = 0.25, k = 0.2, T = 155N, find aG. No slipping, aG = 0.45  (4) rout rin To check the condition of no slipping:

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