Name: angular momentum relative to point p
Uploaded: 2024-03-07T13:22:28.000Z
Duration: 1 min 11 s
Channel: JoVE

Considérons un corps rigide de masse 'm' et un centre de masse au point G, tournant dans un référentiel inertiel.
En un point arbitraire P, le moment angulaire est déterminé en prenant le produit vectoriel du vecteur position et du vecteur moment linéaire pour chaque élément de masse.
La vitesse d'un élément de masse est composée de sa vitesse de translation et de la vitesse relative causée par la rotation du corps.
En substituant l’équation du vecteur vitesse dans l’équation du moment angulaire, en développant le produit vectoriel et en l’intégrant sur toute la masse, on obtient le moment angulaire total autour du point P.
Ici, si le point P est choisi comme centre de masse du corps, alors la première intégrale devient nulle. Si le point P est choisi comme point fixe, alors le terme de vitesse linéaire disparaît.
Pour tout autre point arbitraire, l’intégrale peut être simplifiée. Ici, le premier terme donne le moment dû à la quantité de mouvement linéaire, et le second terme donne le moment angulaire au centre de masse de l’objet.

moment angulaire autour de tout point arbitraire

Angular Momentum about an Arbitrary Axis

Imaginez un corps rigide avec une masse notée « m », qui a son centre de masse au point G et tourne autour d'un cadre de référence inertiel. Le moment angulaire en un point arbitraire P peut être calculé en prenant le produit croisé du vecteur position et du vecteur de moment linéaire pour chaque élément de masse individuel.

La vitesse d'un élément de masse comprend sa vitesse de translation et la vitesse relative provoquée par la rotation du corps. La substitution de l'équation de vitesse dans l'équation du moment angulaire, l'expansion du produit vectoriel et l'intégration sur toute la masse donnent le moment angulaire total autour du point P.

Si le point P est sélectionné comme le centre de masse du corps, alors la première intégrale devient nulle à mesure que le vecteur position devient nul. Si le point P est choisi comme point fixe, alors le terme de vitesse linéaire disparaît. Pour tout autre point arbitraire, l'intégrale peut être simplifiée. Dans ce cas, le premier terme fournit le moment dû au moment linéaire, tandis que le deuxième terme donne le moment cinétique au centre de masse de l'objet. Cette approche permet une compréhension complète du moment cinétique par rapport à différents points d'un corps en rotation.

Moment angulaire autour de tout point arbitraire

Considérons un corps rigide de masse 'm' et un centre de masse au point G, tournant dans un référentiel inertiel.
En un point arbitraire P, l’angulaire ...

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Mechanical Engineering

Génie mécanique

Unit 1

Unité 1

3-Dimensional Kinetics of a Rigid Body

Cinétique tridimensionnelle d'un corps rigide

KEY TERMS AND CONCEPTS

TERMES ET CONCEPTS CLÉS

angular momentum relative to point p

Angular momentum relative to point P is found by adding the motion of every mass element in a rigid body. The body has mass m and a center of mass at point G. It rotates in an inertial reference frame, and the angular momentum at P comes from the cross product of each position vector and its linear momentum.

To build the full expression, the velocity of each mass element is written as two parts. One part is the translational velocity of the body. The other part is the relative velocity caused by rotation. Substituting this velocity into the angular momentum equation, expanding the cross product, and integrating over the entire mass gives the total angular momentum about point P.

The choice of point P changes the result in useful ways. If P is the center of mass, the first integral becomes zero because the position vector is zero. If P is a fixed point, the linear velocity term disappears. For any other arbitrary point, the integral can still be simplified. In that case, the first term gives the moment from linear momentum, and the second term gives the angular momentum at the center of mass of the object.

Angular Momentum Relative to Point P

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Angular momentum relative to point P is found by adding the motion of every mass element in a rigid body. The body has mass m and a center of mass at point G. It rotates in an inertial reference frame, and the angular momentum at P comes from the cross product of each position vector and its linear momentum. To build the full expression, the velocity of each mass element is written as two parts. One part is the translational velocity of the body. The other part is the relative velocity caused...

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Learn how angular momentum is calculated about an arbitrary point in a rigid body, and how the center of mass or a fixed point changes the result.

Angular Momentum Relative to Point P | JoVE K12

JoVE Core Mechanical Engineering offers concise, easy-to-understand animated videos covering key topics such as equilibrium, forces, truss analysis, and structural mechanics. Explore their real-world applications, and witness these concepts in action through scientist-led experiments.

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Angular Momentum Relative to Point P

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