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

Verschiedene physikalische Größen der technischen Mechanik, die zur Beschreibung der Bewegung des Objekts verwendet werden, werden entweder mit Skalaren oder Vektoren gemessen.
Skalare sind physikalische Größen, die durch die Größe beschrieben und durch einen numerischen Wert mit einer physikalischen Einheit dargestellt werden, entweder positiv oder negativ. Länge, Geschwindigkeit, Distanz und Zeit sind einige Beispiele.
Vektoren sind physikalische Größen, die durch einen Pfeil beschrieben werden, der sowohl Größe als auch Richtung hat. Die Länge des Pfeils stellt die Größe dar, und der Winkel zwischen dem Vektor und einer festen Achse stellt die Richtung seiner Wirkungslinie dar.
Sie werden in fetten Buchstaben oder mit Hilfe eines Pfeils über dem Buchstaben dargestellt, während ihre Größen durch Kursivschrift dargestellt werden. Einige Beispiele sind Geschwindigkeit, Beschleunigung und Kraft.
Stellen Sie sich zum Beispiel einen beweglichen Aufzug vor. Die Abmessungen und die Masse des Auftriebs sind die skalaren Größen, während die Geschwindigkeit und das Gewicht des Auftriebs Vektorgrößen sind, da sie sowohl eine Größe als auch eine Richtung haben.

<ol>
	<li>Hibbeler, R.C. (2016). Technische Mechanik \u2012 Statik und Dynamik. Hoboken, New Jersey: Pearson Prentice Hall. Seite 17</li>
</ol>

skalare und vektoren

Skalare Größen mit den gleichen physikalischen Einheiten können nach den üblichen Rechenregeln der Algebra für Zahlen addiert oder subtrahiert werden. Zum Beispiel dauert eine Klasse, die 10 Minuten früher endet als 50 Minuten, 50 Minuten − 10 Minuten = 40 Minuten. Ebenso ergibt eine Portion Mais mit 60 Kalorien gefolgt von einer Portion Donuts mit 200 Kalorien insgesamt 60 Kalorien + 200 Kalorien = 260 Kalorien Energie. Wenn wir eine skalare Größe mit einer Zahl multiplizieren, erhalten wir die gleiche skalare Größe, jedoch mit einem größeren (oder kleineren) Wert. Wenn zum Beispiel das Frühstück von gestern 200 Kalorien Energie hatte und das Frühstück von heute viermal so viel Energie wie gestern hat, hat das heutige Frühstück 4 × 200 Kalorien = 800 Kalorien Energie. Zwei skalare Größen können auch miteinander multipliziert oder dividiert werden, um eine abgeleitete skalare Größe zu bilden. Zum Beispiel, wenn ein Zug eine Strecke von 120 km in 1 Stunde zurücklegt, beträgt seine Geschwindigkeit 120.000 m/3600 s = 33 m/s, wobei die Geschwindigkeit eine abgeleitete skalare Größe ist, die durch Division von Strecke durch Zeit erhalten wird.

Auf der anderen Seite ist eine Vektorgröße eine physikalische Größe, die sowohl einen Betrag als auch eine Richtung hat. Ein Vektor kann graphisch durch einen Pfeil dargestellt werden. Die Länge des Pfeils symbolisiert den Betrag des Vektors, während der Winkel zwischen ihm und einer festen Achse seine Wirklinie bestimmt. Die Spitze des Pfeils stellt die Richtung dar, in die der Vektor zeigt. Beispiele für Vektorgrößen sind Verdrängung, Geschwindigkeit, Position, Kraft und Drehmoment.

Stellen wir uns vor, wir geben einem Freund auf einer Wanderung Anweisungen für einen Rastpunkt, der 6 km vom Zelt entfernt ist. Der einfachste Weg besteht darin, anzugeben, in welche Richtung der genaue Ort erreicht werden soll; zum Beispiel ist "6 km südöstlich" hilfreicher. Diese Größe ist die Verdrängung des Wanderers.

Zwei Vektoren sind gleich, wenn sie den gleichen Betrag und dieselbe Richtung haben. Zwei Vektoren mit identischer Richtung werden als parallele Vektoren bezeichnet. Wenn ein Vektor jedoch genau entgegengesetzt, also um genau 180°, zum ersten Vektor zeigt, werden sie als antiparallel bezeichnet. Zwei Vektoren mit senkrechter Richtung zueinander werden als orthogonal bezeichnet.

Skalare und Vektoren

In der Mechanik können häufig verwendete Begriffe wie Kraft, Geschwindigkeit, Geschwindigkeit und Arbeit entweder als skalare oder Vektorgrößen klassifiziert werden. Ein Skalar ist ein physikalischer ...

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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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Scalar vs Vector Quantities in Mechanics

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