See image... why is it that in part 1 the answer is negative but in part 2 it is added instead of subtracted?
I thought because I got a negative in part 1 I would have to subtract in part 2 but the solution shows otherwise.
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1 Answer
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In Part 1 the rotation is clockwise WRT rigid disk B if we chose plane B as reference and look at it in such a way that the steel assembly is coming out of that plane. This viewpoint is used in line 1 of your notes to calculate the $\phi_{C/B}$.
However, if we look from behind B toward A the $\phi_{C/B}$ is counterclockwise and positive.
This is the view used for total rotation(line 2 of your notes). Hence both rotations are counterclockwise and additive!
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$\begingroup$ I must be missing something, so when doing part 2 should I just be looking at the blue rotation and not the calculated ones (ie. T_ab and T_cb)? $\endgroup$ Commented Oct 11, 2023 at 1:59
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$\begingroup$ You use the calculated value.s magnitude sure, but because you are now using a different reference frame 180 degrees rotated, you have to respect the direction in this new reference frame. Either that or you can keep your reference frame the same plane B, with the steel bar coming out of the plane. then both rotation of the cylinder and solid ber are clockwise and negative. so we add the sum of 2 negative angles. Rotation is like a vector. It has magnitude and direction. If you change your reference frame 180 degrees the sign of the rotation angle changes! It is only a matter of consistency! $\endgroup$– kamranCommented Oct 11, 2023 at 6:20
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$\begingroup$ Omg I see it now, thank you! $\endgroup$ Commented Oct 11, 2023 at 22:56