Question

Free body diagram: 24 0.5r 0.5r No slip (a) An ec centric disk is rotating on the ground as shown in the figure above. The disk has radius r. The distance between the center of mass of the disk (denoted as C) to its geometric center (denoted as O) is 1 r. The angle of rotation of the disk is θ and the displacement at point O is x. The disk has mass m. The moment of inertia with respect to its center of mass is Jc- mr2. A spring force Kx is applied to point o. Follow the following procedure to derive the EOM ofthis dynamic system: (15%) Step 1 (elemental equations): (11%) (Easy) Euler equation of rotation around C: 24 Newton's second law for translational motion at the center of mass C: Kinematic constraints: x, x-05-r-sin θ -0.5 . r . cos θ X- 2 (eliminate the intermediate variables and derive the EOM in terms of θ): (4%) (Hard)

Answer 1

In the given problem the disk is a combination of rectilinear and rotational motion.

Rectilinear motion in terms of X and y

Rotational motion in terms of angular displacement

For deriving the equation of motion in terms of angular displacement it consists inertial moments and reaction motion with respect to the reference point.here the reference point is centre of mass c

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