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# hw5solution - Homework 5 Solution 1(a The system is shown...

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Homework 5 Solution 1. (a) The system is shown here again with additional variables: k O m m r 4 r k T A θ B x φ The total kinetic energy has three parts: rotational kinetic energy of the rod, as well as translational and rotational kinetic energies of the disk: T 1 2 J 0 ̇ 2 1 2 mx ̇ 2 1 2 J ̇ 2 The potential energy also has three parts: deformation in the linear spring, twisting in the torsional spring, and the rod’s gravitational potential energy: U 1 2 k T 2 1 2 kx 2 mg 2 r cos Note that the variable x is the displacement at the center of the disk, and the angle is the rotation of the disk. We can relate the motion of the disk to the rotation of the rod from kinematics since the disk rolls without slipping. Both points A and B have the same displacement: 4 r 2 r 2 The displacement at the disk’s center for rolling without slipping is x r 2 r So the total energy can now be written as

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hw5solution - Homework 5 Solution 1(a The system is shown...

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