Question

1. The figure shows an object, that includes a thin rod with mass m and length 2a, located on the y axis and centered on the origin O. Attached to the end points of the rod is half of a thin circular hoop with mass M and radius a. Note: M is the mass of the part of the hoop shown in the figure. The object is located completely within the xy plane. The +z axis is perpendicular to the drawing throguh O. The dashed line is the line y = x in the xy plane. This is the axis of rotation of the object in this problem. a -a a X (a) Identify which elements of the inertia tensor are equal to zero. (As usual, please include your reasoning.) (b) Derive the value of all other elements of the inertia tensor in terms of m, M, and a. (c) Calculate the angle between the angular momentum with respect to O and the angular velocity vector, as the frame spins with angular velocity w about the line y = x (the dashed line in the figure).

          1. The figure shows an object, that includes a thin rod with mass m and length 2a, located on the y axis
and centered on the origin O. Attached to the end points of the rod is half of a thin circular hoop with
mass M and radius a. Note: M is the mass of the part of the hoop shown in the figure. The object is
located completely within the xy plane. The +z axis is perpendicular to the drawing throguh O. The
dashed line is the line y = x in the xy plane. This is the axis of rotation of the object in this problem.
a
-a
a
X
(a) Identify which elements of the inertia tensor are equal to zero. (As usual, please include your
reasoning.)
(b) Derive the value of all other elements of the inertia tensor in terms of m, M, and a.
(c) Calculate the angle between the angular momentum with respect to O and the angular velocity
vector, as the frame spins with angular velocity w about the line y = x (the dashed line in the
figure).

1 the figure shows an object that includes a thin rod with mass m and length 2a located on the y axis and centered on the origin o attached to the end points of the rod is half of a thin cir 78279

Added by Cynthia B.

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