7. (a) Derive the Euler equations for rigid body motion. (8 marks) (b) A disc rotor has a mass of 30 kg and a radius of

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7 A Derive The Euler Equations For Rigid Body Motion 8 Marks B A Disc Rotor Has A Mass Of 30 Kg And A Radius Of 1 (328.87 KiB) Viewed 15 times

7. (a) Derive the Euler equations for rigid body motion. (8 marks) (b) A disc rotor has a mass of 30 kg and a radius of 125 mm about its polar axis, while the radius of gyration about its diametral axis is 75 mm. This rotor is pressed onto a shaft but, due to incorrect boring the angle between the polar axis and the axis of rotation is 0.25º. The shaft is carried between bearings 200 mm apart and the speed of rotation is 6000 rpm. (i) Sketch the disc. Show clearly the local axes you have defined. Show/state how the sign of directions are defined. Assign a direction of rotation of the disc about its rotation axis. (4 marks) Determine the resulting dynamic moment. (4 marks) What direction is this moment and ab what axis. (2 marks) Determine the force on the bearings. (2 marks) (ii) (iii) (iv)