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Angular Moment
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The key to developing the concepts that allow defining what generates rotational motion are related to the angular momentum as the product of the moment of inertia and the angular velocity of the object.
ID:(1407, 0)
Angular Moment
Description
The key to developing the concepts that allow defining what generates rotational motion are related to the angular momentum as the product of the moment of inertia and the angular velocity of the object.
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(ID 3251)
Just as the relationship between the speed ($v$) and the angular Speed ($\omega$) with the radius ($r$) is expressed by the equation:
| $ v = r \omega $ |
we can establish a relationship between the angular Momentum ($L$) and the moment ($p$) in the context of translation. However, in this case, the multiplicative factor is not the arm ($r$), but rather the moment ($p$). This relationship is expressed as:
| $ L = I \omega $ |
(ID 9874)
Examples
As with the relationship between linear velocity and angular velocity,
| $ v = r \omega $ |
we can establish a connection between angular momentum and translational momentum. However, in this scenario, it's the radius that multiplies the momentum, not the angular momentum, which is:
| $ \vec{L} = \vec{r} \times \vec{p} $ |
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(ID 10290)
The moment ($p$) was defined as the product of the inertial Mass ($m_i$) and the speed ($v$), which is equal to:
| $ p = m_i v $ |
The analogue of the speed ($v$) in the case of rotation is the instantaneous Angular Speed ($\omega$), therefore, the equivalent of the moment ($p$) should be a the angular Momentum ($L$) of the form:
| $ L = I \omega $ |
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the inertial Mass ($m_i$) is associated with the inertia in the translation of a body, so the moment of Inertia ($I$) corresponds to the inertia in the rotation of a body.
(ID 3251)
The angular Momentum ($L$) is the analogue of the moment ($p$). Therefore, just as in translational motion it corresponds to the product of the inertial Mass ($m_i$) and the speed ($v$), in rotational motion it is obtained from the moment of Inertia ($I$) and the angular Speed ($\omega$), according to the relation:
| $ L = I \omega $ |
(ID 9874)
In one dimension, the angular Momentum ($L$) together with the arm ($r$) and the moment ($p$) equals
| $ L = r p $ |
the angular Momentum ($L$) can be generalized to more dimensions as the angular Momentum (Vector) ($vec{L}$). Since both parameters the radius (vector) ($\vec{r}$) and the momento (vector) ($\vec{p}$) are vectorial, the definition of the angular Momentum (Vector) ($vec{L}$) is constructed through a cross product in the form:
| $ \vec{L} = \vec{r} \times \vec{p} $ |
(ID 4774)
ID:(1407, 0)