This is true for all vectors: angular momentum, angular velocity, displacement, acceleration, magnetic field, whatever. Whenever we want to express a vector as viewed from the primed frame, we can determine its components in this frame by multiplying the version of the vector in the unprimed frame by the same rotation matrix. Let's refer to the rotation matrix as R. Rank-two tensors transform differently under rotations. It is tempting to think that the rule should be / = R/, but it isn't. Here's a quick derivation of the transformation rule. In the following, R" is the inverse of R and 1 is the identity matrix. Oh-recall that matrix multiplication is associative: (AB)C = A( BC). I = 10 RI = RIO. Since I' = RI, Ra= @, and R-1R=1, I' = RI = RIG = R/1@ = RI\\R-R)@ =(RIR-1 )( RO) = (RIR-1). As a result, I' = \\RIR-1) @ = I'd so that !' = RIR-1. That is how a rank-two tensor transforms under rotations. (d) For the case that 0= 1800, R = 0 1 0 and R-1 = R. Use this to transform the inertia 0 0 -1 tensor for the object as drawn in the above figure to its form in a frame rotated around the y axis by 180. Show that this agrees with your result in part (c)