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# Rigid Body Dynamics

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Problem 1 : To determine moment of inertia about different axes of rotation of a circular disc of given radius of gyration.

Problem 2 : A two pulley system. To determine acceleration, tension in the cable etc.

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Step by step solution provided. Rigid body dynamics problems are examined.

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Problem 1

Y C

b

X
B
2'

a a b
C A
5'

B

By definition, the radius of gyration of an object about a given axis of rotation is the perpendicular distance of a point from the axis such that the moment of inertia of whole mass of the object assumed concentrated at the point is same as the moment of inertia about the given axis with the actual distribution of mass. In the given problem the axis of rotation for the given radius of gyration is not specified. Hence, we assume the axis as the Z axis passing through the centre of the disc.

a) From the definition of radius of gyration above, Moment of inertia about the Z axis = Mass of the disc x (Radius of gyration)2 = (50/32.2)x0.752 = 0.873 ...

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