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

Varie grandezze fisiche in meccanica ingegneristica utilizzate per descrivere il movimento dell'oggetto sono misurate utilizzando scalari o vettori.
Gli scalari sono grandezze fisiche descritte dalla grandezza e rappresentate da un valore numerico con un'unità fisica, positiva o negativa. Lunghezza, velocità, distanza e tempo sono alcuni esempi.
I vettori sono grandezze fisiche descritte da una freccia che ha sia grandezza che direzione. La lunghezza della freccia rappresenta la magnitudine e l'angolo tra il vettore e un asse fisso rappresenta la direzione della sua linea d'azione.
Sono rappresentati in grassetto, o con l'aiuto di una freccia sopra la lettera, mentre le loro grandezze sono rappresentate mettendo in corsivo la lettera. Alcuni esempi sono la velocità, l'accelerazione e la forza.
Ad esempio, considera un ascensore in movimento. Le dimensioni e la massa della portanza sono le grandezze scalari, mentre la velocità e il peso della portanza sono grandezze vettoriali in quanto hanno sia una grandezza che una direzione.

<ol>
	<li>Hibbeler, R.C. (2016). Ingegneria Meccanica \u2012 Statica e Dinamica. Hoboken, New Jersey: Pearson Prentice Hall. pagg. 17</li>
</ol>

scalari e vettori

In meccanica, termini comunemente usati come forza, velocità e lavoro possono essere classificati come grandezze scalari o vettoriali. Uno scalare è una grandezza fisica che può essere descritta solo dalla sua magnitudine e non richiede componenti direzionali. Esempi di grandezze scalari sono massa, area e lunghezza.

 Le grandezze scalari con le stesse unità fisiche possono essere sommate o sottratte secondo le usuali regole algebriche per i numeri. Ad esempio, una lezione che finisce 10 minuti prima di 50 minuti dura 50 minuti - 10 minuti = 40 minuti. Allo stesso modo, un servizio di mais da 60 calorie seguito da un servizio di ciambelle da 200 calorie dà 60 calorie + 200 calorie = 260 calorie di energia. Quando moltiplichiamo una grandezza scalare per un numero, otteniamo la stessa grandezza scalare ma con un valore più grande (o più piccolo). Ad esempio, se la colazione di ieri aveva 200 calorie di energia e la colazione di oggi ha quattro volte più energia di ieri, allora la colazione di oggi ha 4 x 200 calorie = 800 calorie di energia. Due grandezze scalari possono anche essere moltiplicate o divise tra loro per formare una grandezza scalare derivata. Ad esempio, se un treno percorre una distanza di 120 km in 1 ora, la sua velocità è di 120.000 metri/3600 secondi = 33 metri/secondo, dove la velocità è una grandezza scalare derivata, ottenuta dividendo la distanza per il tempo.

D'altra parte, una grandezza vettoriale è una grandezza fisica che ha sia magnitudine che direzione. Un vettore può essere rappresentato graficamente utilizzando una freccia. La lunghezza della freccia simboleggia la magnitudine del vettore, mentre l'angolo tra essa e un asse fisso determina la sua linea di azione. La testa della freccia rappresenta la direzione in cui il vettore sta puntando. Esempi di grandezze vettoriali includono lo spostamento, la velocità, la posizione, la forza e il momento torcente.

Considera di dare indicazioni a un amico durante un'escursione per raggiungere un punto di ristoro a 6 km dalla tenda. Il modo più semplice sarà identificare in quale direzione raggiungere la posizione esatta; ad esempio, 6 km a sudest sarà più utile. Questa grandezza è lo spostamento dell'escursionista.

Due vettori sono uguali se hanno la stessa magnitudine e la stessa direzione. Due vettori con direzioni identiche sono detti vettori paralleli. Tuttavia, se un vettore punta nella direzione opposta, esattamente a 180°, rispetto al primo, si dicono antiparalleli. Due vettori con direzioni perpendicolari tra loro sono detti vettori ortogonali.

Scalari e Vettori

In meccanica, termini di uso comune come forza, velocità, velocità e lavoro possono essere classificati come quantità scalari o vettoriali. Uno scalare è 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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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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Scalar vs Vector Quantities in Mechanics

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