Question

As shown in Fig. 3, a homogenous disk of mass m = 3.5 kg rotates at the constant rate ?1 = 15 rad/s with respect to arm ABC, which is welded to a shaft DCE rotating at the constant rate ?2 = 8.5 rad/s. Determine (a) the angular momentum of the disc about point C (b) the couple of body representing the dynamic reactions at supports D and E and (c) the kinetic energy of the system. Both angular momentum and couple are vector quantity. Indicate clearly magnitude and direction of the parameters. Draw appropriate free body diagrams and reference system to clearly illustrate your logical solution steps.

Q3. As shown in Fig. 3, a homogenous disk of mass m = 3.5 kg rotates at the constant rate W1 = 15 rad/s with respect to arm ABC, which is welded to a shaft DCE rotating at the constant rate W2 = 8.5 rad/s. Determine (a) the angular momentum of the disc about point C (b) the couple of body representing the dynamic reactions at supports D and E and (c) the kinetic energy of the system. Both angular momentum and couple are vector quantity. Indicate clearly magnitude and direction of the parameters. Draw appropriate free body diagrams and reference system to clearly illustrate your logical solution steps. r = 200 mm 200 mm 200 mm 300 mm 300 mm Fig. 3

Answer 1

Consider the sustem as shown in the figure. We know that angular Ay momentum of a solid disk about ito centre a is given as a Io e more (where xio - radius of disc) - (a.) Angulur mom entum of disa about a The disc is at a distance from the -point c in z direction and also perpendicular to n-ania we will have to apply both paralled and perpendicular anis theorem Initially we and the moment of inerna / - of disc about a i parallel ane at a distance 200_m_m_fremite loomonas (mol)ogo e Corange am Cor)? IA" from someone my nam m?, mm? още

4 1 Now, we and the moment of inertia of disa about ito perpendicular anis. we know that (molla e molly +(Molly and (Molly e Molly fue a disc ----- 2 Imre __) (holla? (Molly a (Mollu 2 3x 3.5 x 200 x 183 ² 0.105 kg m² now? (6) The pet force due to rotation ! of disc at A is given by far (mrw - mg) faz o 191.165 N_ This fa when translated at a gives a moment given by me a fax (200 mm) 2 24. 69 Nm is at the centre of both supports, - Dynamic reaction at De dynamic reaction at E 2d Me 12315NM__ - (c) kinetic energy of septeme d Ivo, + 1 IC w 2 - where I and fc are mol about A and resp. :€ 2.2 (mans my wo? + 63mmy wiele cresp. ko €. = 7.07 + 9.79 111.665 J 1