Question

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Figure 3: A rotating shaft with the welded homogeneous solid cube of mass m with the size of the edge 2a. 6. A weightless (light) shaft AB of length 6a has a homogeneous solid cube of mass m with the size of the edge equal to 2a welded to the shaft along the edge CD, see Figure 3. The system is supported by bearings at A and B and rotates about AB at 2 radians per second. The effects of gravity are neglected throughout the calculation. a) Find the centre of mass with reference to the origin at A for the whole device. 2 marks] b) Find the total inertia matrix for the system with reference to the origin at A. (6 marks) c) Obtain the forces exerted on the device by the bearings at A and B. 12 marks Total: 20 marks

Answer 1

CD Jo Toa c* (4,4 ) sa 2a -2a 2ん 5ん_1n. a b ζα 5A-2a За

3 9 3 392 +32 x 500 -- "Ma 424 Mar No x 125 て 125 125 м

2a V За о За о 64 a5p Ma

72 2 2.a 了-了 g o 53-3 Z20 p - 392 a a-4 ろ2 392 5 X 424 5_3 ←-24 1 53 Ma 4 .

2a 5a -2a. 4 Ma 2a)?

2a За 2 8a3 2a 5a2a За 0 (2«) Mo 0

MIろ ΣΣ 3-3 M そ

TO -e A. 씨 B