Jump to first page 1 Chapter 7 Plane Kinetics of Rigid Body

Jump to first page 2 Moment of inertia of a rigid body about an axis. y x I G is the moment of inertia about G.

Jump to first page 3 Example : Moment of inertia of a cylinder about the axis. drdr r L a

Jump to first page 4 Parallel axis theorem : I o = I G + mh 2

Jump to first page 5 Example h a

Jump to first page 6 For a thin plate, the moment of inertia about the z-axis is : I z = I x + I y z y x x y

Jump to first page 7 Radius of gyration is defined as: Example: Radius of gyration of a circular disc. a R g = (I G /m) 1/2

Jump to first page 8 Self-learning exercise b dxdx b dxdx

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

Jump to first page 11 Example: Find T 1, T 2 and a G when BF is cut. 0.3 m Cut 0.1m At the moment when the string at B is cut, v A = 0 3 equations v.s. 3 unknowns

Jump to first page 12 Example A compound wheel has an inner wheel with a radius r in =150 mm and an outer wheel of radius r out = 450 mm. Radius of gyration about G is R g = 0.25m. If m = 70 kg,  s = 0.25,  k = 0.2, T = 155N, find a G. No slipping, a G = 0.45  (4) To check the condition of no slipping: r out r in