When I do some math, how could I know which rotating moment should be minus sign or plus sign?
For example, T= - I* theta, I don't know why. Is it minus for the clockwise rotation and plus for the counterpart?
I just think T and I have absolutely different directions (T is counterclockwise and I is clockwise), so my thought is T - I* theta =0 ('cause their rotating direction is opposite) and then T = I* theta.
However, my teacher said: my answer is wrong!
Please someone can tell me why why why and prove I'm wrong. Please Please Please~
Answers:
From what I use in Engineering: all angles are measured as positive anti-clockwise.
Therefore a rotation in the clockwise direction of magnitude 5 degrees, would be a rotation of -5degrees. Does that make sense? So although it a clockwise rotation of 5 degrees, it goes into the equation as -5 degrees.
So if the total roation is 0, then T+I*theta=0, T=-I*theta
It might help if you draw both T and I as anticlockwise rotations, but give I a negative value.
I thought it was just a convention. Anti-clockwise angles are posititive.
The convention could also be the opposite and the maths would still be correct if applied consistently.
The best analogy I can think of is driving on the left or right for a particular country. It works as long as everyone follows the same convention.
Can you imagine what would happen if we could all decide on which side of the road to drive on?
The absolute value of the those angles could be the same, but the directions where they are rotating are different. As an example, you could walk 10 ft to the north or you could also walk 10 ft to the south. In both situations you are walking 10 ft but that doesn't mean you are going to the same place. The same with angles.
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I just think T and I have absolutely different directions (T is counterclockwise and I is clockwise), so my thought is T - I* theta =0 ('cause their rotating direction is opposite) and then T = I* theta.
However, my teacher said: my answer is wrong!
Please someone can tell me why why why and prove I'm wrong. Please Please Please~
Answers:
From what I use in Engineering: all angles are measured as positive anti-clockwise.
Therefore a rotation in the clockwise direction of magnitude 5 degrees, would be a rotation of -5degrees. Does that make sense? So although it a clockwise rotation of 5 degrees, it goes into the equation as -5 degrees.
So if the total roation is 0, then T+I*theta=0, T=-I*theta
It might help if you draw both T and I as anticlockwise rotations, but give I a negative value.
I thought it was just a convention. Anti-clockwise angles are posititive.
The convention could also be the opposite and the maths would still be correct if applied consistently.
The best analogy I can think of is driving on the left or right for a particular country. It works as long as everyone follows the same convention.
Can you imagine what would happen if we could all decide on which side of the road to drive on?
The absolute value of the those angles could be the same, but the directions where they are rotating are different. As an example, you could walk 10 ft to the north or you could also walk 10 ft to the south. In both situations you are walking 10 ft but that doesn't mean you are going to the same place. The same with angles.
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