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(Solved): Consider a triangular prism of uniform mass, M, with equilateral triangular faces and rectangular si ...
Consider a triangular prism of uniform mass, M, with equilateral triangular faces and
rectangular sides. Let the rectangular sides have lengths L_(T) and L_(D), where L_(T) are also the
lengths of the edges of the triangular faces. Let point O be at the centroid of the triangle.
Let O be the origin of both a reference frame R that is fixed to the prism and an inertial
frame N. Let {hat(e)_(x),hat(e)_(y),hat(e)_(z)} be the orthonormal basis vectors for frame R. Let {hat(i)_(x),hat(i)_(y),hat(i)_(z)} be
the orthonormal basis vectors for frame N. Let both hat(e)_(z) and hat(i)_(z) be aligned with a z-axis
which goes through the centroid at point Ohat(e)_(x)hat(e)_(y)-plane and hat(i)_(x)hat(i)_(y)-plane-z direction. Let gravity be the only force acting
on the rigid body. Let the points A,B, and C be at the vertices of the prism's triangular
cross-section on the hat(e)_(x)hat(e)_(y)-plane.
AR evaluated at point
O. Give your answer in matrix form.
BR evaluated at point
A. Give your answer in matrix form.
CR evaluated at the
midpoint between points A and B .
DL_(D) is small and the prism is like a flap on a hinge which keeps
BC fixed in frame N.O ?
HO ?
I