Q:

1.1 (a) Use a vector approach to prove that if F = m( d ?/dt) is true for a mass moving with an arbitrary (i.e., nonconstant) velocity relative to a fixed Cartesian coordinate system, the exact same form of force acceleration equation applies in any other Cartesian coordinate system that translates at a constant velocity relative to the first Cartesian coordinate system.

(b) Show that the time rate of change of the angular momentum (i.e., moment of momentum) of a collection of particles is zero whenever all of the particles are moving at a constant velocity relative to the valid coordinate system.

(c) Show that the sum of the moments about an arbitrary point of two collinear forces of equal magnitudes, but oppositely directed, is zero.

(d) Show that if a rigid body is in static equilibrium, any virtual displacement leads to zero virtual work.

(e) Show that if, in connection with an arbitrary virtual displacement, the virtual work of a rigid body is zero, then that body is in static equilibrium.

Q:

1.2 Evaluate the mass moment of inertia at the center of mass about the z axis for a constant density, rectangular parallelepiped whose x, y, z uniform dimensions are, respectively, a, b, c. Hint: Multiple integration is expected.

Q:

1.3 How many degrees of freedom are necessary for the following rigid body systems?

(a) A cylinder...