Name: scalar vs vector quantities in mechanics
Uploaded: 2023-09-22T11:49:38.000Z
Duration: 1 min 22 s
Channel: JoVE

Diverses grandeurs physiques en mécanique de l'ingénierie utilisées pour décrire le mouvement de l'objet sont mesurées à l'aide de scalaires ou de vecteurs.
Les scalaires sont des grandeurs physiques qui sont décrites par une amplitude et représentées par une valeur numérique avec une unité physique, positive ou négative. La longueur, la vitesse, la distance et le temps en sont quelques exemples.
Les vecteurs sont des grandeurs physiques qui sont décrites par une flèche ayant à la fois l’intensité et la direction. La longueur de la flèche représente l’amplitude et l’angle entre le vecteur et un axe fixe représente la direction de sa ligne d’action.
Ils sont représentés en caractères gras, ou à l’aide d’une flèche sur la lettre, tandis que leurs amplitudes sont représentées en italique de la lettre. Quelques exemples sont la vitesse, l’accélération et la force.
Prenons l’exemple d’un ascenseur en mouvement. Les dimensions et la masse de l’ascenseur sont les grandeurs scalaires, tandis que la vitesse et le poids de l’ascenseur sont des quantités vectorielles car elles ont à la fois une amplitude et une direction.

<ol>
	<li>Hibbeler, R.C. (2016). Génie mécanique \u2012 Statique et dynamique. Hoboken, New Jersey : Pearson Prentice Hall. p. 17 [</li>traduction]
</ol>

scalaires et vecteurs

En mécanique, les termes couramment utilisés tels que la force, la vitesse, la vélocité et le travail peuvent être classés comme des quantités scalaires ou vectorielles. Un scalaire est une quantité physique qui peut être décrite par sa magnitude seule et ne nécessite aucune composante directionnelle. Des exemples de quantités scalaires sont la masse, la surface et la longueur. Les quantités scalaires ayant les mêmes unités physiques peuvent être ajoutées ou soustraites selon les règles algébriques habituelles pour les nombres. Par exemple, une classe qui se termine 10 minutes plus tôt que 50 minutes dure 50 minutes – 10 minutes = 40 minutes. De même, une portion de maïs de 60 calories suivie d'une portion de beignets de 200 calories donne 60 calories + 200 calories = 260 calories d'énergie. Lorsque nous multiplions une quantité scalaire par un nombre, nous obtenons la même quantité scalaire mais avec une valeur plus grande (ou plus petite). Par exemple, si le petit–déjeuner d'hier contenait 200 calories d'énergie et que le petit–déjeuner d'aujourd'hui a quatre fois plus d'énergie que celui d'hier, le petit–déjeuner d'aujourd'hui contient 4 x 200 calories = 800 calories d'énergie. Deux quantités scalaires peuvent également être multipliées ou divisées l'une par l'autre pour former une quantité scalaire dérivée. Par exemple, si un train parcourt une distance de 120 km en 1 heure, sa vitesse est de 120 000 m/3600 s = 33 m/s, où la vitesse est une quantité scalaire dérivée obtenue en divisant la distance par le temps. D'autre part, une quantité vectorielle est une quantité physique qui a à la fois une magnitude et une direction. Un vecteur peut être représenté graphiquement à l'aide d'une flèche. La longueur de la flèche symbolise la magnitude du vecteur, tandis que l'angle entre la flèche et un axe fixe détermine sa ligne d'action. La tête de la flèche représente la direction dans laquelle le vecteur pointe. Des exemples de quantités vectorielles comprennent le déplacement, la vitesse, la position, la force et le couple. Considérons donner des indications à un ami lors d'une randonnée pour un point de repos situé à 6 km de la tente. Le moyen le plus facile sera d'identifier dans quelle direction atteindre l'emplacement exact ; par exemple, 6 km au sud–est sera plus utile. Cette quantité est le déplacement du randonneur. Deux vecteurs sont égaux s'ils ont des magnitudes égales et la même direction. Deux vecteurs ayant des directions identiques sont dits parallèles. Cependant, si un vecteur pointe dans la direction opposée, exactement à 180 degrés, du premier vecteur, ils sont dits antiparallèles. Deux vecteurs ayant des directions perpendiculaires l'un par rapport à l'autre sont dits vecteurs orthogonaux.

Scalaires et Vecteurs

En mécanique, les termes couramment utilisés comme force, vitesse, vitesse et travail peuvent être classés comme des quantités scalaires ou vectorielles. Un scalaire est un ...

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Scalar and Vectors

scalar vs vector quantities in mechanics

Scalar and vector quantities are two main ways to describe physical quantities in mechanics. Common examples include force, speed, velocity, and work. Some of these are scalars, and others are vectors.

A scalar is a quantity that has magnitude only. It does not need direction. Mass, area, and length are examples of scalar quantities. Scalars with the same units can be added or subtracted like ordinary numbers. A class that ends 10 min earlier than 50 min lasts 50 min minus 10 min, which is 40 min.

Scalars can also be multiplied by a number. If yesterday’s breakfast had 200 calories of energy and today’s breakfast has four times as much, then today’s breakfast has 800 calories of energy. Two scalars can also be multiplied or divided to make another scalar quantity. For example, a train that covers 120 km in 1 h has a speed of 120,000 m/3600 s, or 33 m/s. That speed is a derived scalar quantity.

A vector has both magnitude and direction. Vectors are often shown with arrows. The arrow length shows the magnitude. The angle with a fixed axis shows the line of action, and the arrowhead shows the direction. Displacement, velocity, position, force, and torque are examples of vector quantities.

Direction matters in everyday situations. If a hiking rest point is 6 km from a tent, saying 6 km southeast is more useful than saying only 6 km. That gives the hiker displacement, which is a vector. Two vectors are equal if they have the same magnitude and the same direction. Vectors with the same direction are parallel. Vectors that point exactly 180° apart are antiparallel. Vectors that meet at right angles are orthogonal.

Scalar vs Vector Quantities in Mechanics

scalar and vectors

Scalar and vector quantities are two main ways to describe physical quantities in mechanics. Common examples include force, speed, velocity, and work. Some of these are scalars, and others are vectors. A scalar is a quantity that has magnitude only. It does not need direction. Mass, area, and length are examples of scalar quantities. Scalars with the same units can be added or subtracted like ordinary numbers. A class that ends 10 min earlier than 50 min lasts 50 min minus 10 min, which is 40...

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Learn how scalar and vector quantities differ in mechanics, with clear examples of magnitude, direction, displacement, speed, and force for high school science.

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Scalar vs Vector Quantities in Mechanics

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