Sign of momentum/angular momentum?
How do you choose the sign of the momentum or the angular momentum?
Below is an image for better understanding:
Body 1 with mass m1 is connected to a fixed support via a massless rod. Body 1 rotates around support A with angular velocity w1 until it encounters body 2 at point 2. We are looking for the angular velocity of body 2 after the impact from body 1.
For this purpose, the momentum and angular momentum theorems are defined as shown in the figure.
My question: How do you know how to choose the sign of the momentum and angular momentum theorems?
I have also seen examples where the momentum had a positive sign and the angular momentum a negative sign, or the other way around.
So how do I know that both must have a negative sign?
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Angular speed and rotational pulse are defined in the same direction. So if you define the angular velocity in such a way that it is positive against the clockwise direction, then the rotational pulse is also positive when the body rotates counterclockwise.
Here, body 2 rotates clockwise after impact and thus has a sign opposite to the angular velocity.
Thank you for your answer. I could apply and understand your explanation.
I have now added my question, perhaps you can help me with this example.
In the second example, a pendulum (consisting of a dot mass m1 and a mass-bearing rod, likewise with mass m1) strikes the above support. The angular velocity is positively defined counterclockwise, the body also rotates counterclockwise. Shouldn't the impulse have a positive sign?
And can you possibly explain to me how to define the sign of normal impulse?
Well, if either both are very rigid, then it can come (glow I at least) that the body 1 bounces off at the mass m2 as if one throws a rubber ball against the wall, since the ball also transmits its impulse to the wall, but still flies away. Here, however, the reason is that the wall (ie m2) is much larger than m1.
But that would at least explain why the rotary pulse (just like the angular velocity) is negative after impact
The rotary pulse vector shows in the same direction as the angular velocity, ie in 2 the rotational pulse is positive. I don't know why he should be negative.
The sign of the pulse is coupled to the sign of the speed. Shock 2 bodies obliquely together you have to count in x, y components.