Q2. Figure 2 shows a thin, uniform, circular disc of radius R, centre of mass G...

Transcribed Image Text:

Q2. Figure 2 shows a thin, uniform, circular disc of radius R, centre of mass G and mass M. The disc is mounted onto a uniform horizontal slender shaft of negligible mass and negligible diameter and of length L. The disc rotates relative to the horizontal shaft with a constant angular velocity, as shown. The shaft is supported by a frictionless pivot at O. Gravity is acting vertically downward and its acceleration is g m/s². It is observed that when the shaft is released from rest in the horizontal position that the disc precesses about pivot with an angular velocity 22, as shown. (a) Draw the Free Body Diagrams of the system. (b) Write all the equations of motions of the disc. [7marks] [8marks] (c) Determine the expression for the precessional angular velocity , of the disc. [10marks] Y A af. 9 L Jove »Z Q2. Figure 2 shows a thin, uniform, circular disc of radius R, centre of mass G and mass M. The disc is mounted onto a uniform horizontal slender shaft of negligible mass and negligible diameter and of length L. The disc rotates relative to the horizontal shaft with a constant angular velocity, as shown. The shaft is supported by a frictionless pivot at O. Gravity is acting vertically downward and its acceleration is g m/s². It is observed that when the shaft is released from rest in the horizontal position that the disc precesses about pivot with an angular velocity 22, as shown. (a) Draw the Free Body Diagrams of the system. (b) Write all the equations of motions of the disc. [7marks] [8marks] (c) Determine the expression for the precessional angular velocity , of the disc. [10marks] Y A af. 9 L Jove »Z