Name: resolving forces in moment calculations
Uploaded: 2023-09-22T11:49:21.000Z
Duration: 1 min 20 s
Channel: JoVE

Il principio dei momenti, o teorema di Varignon, descrive l'equilibrio di un corpo rigido sotto l'azione delle forze.
Afferma che il momento di una forza attorno a un punto è uguale alla somma dei momenti delle componenti della forza attorno al punto.
Il momento di una forza in un punto è il prodotto della distanza perpendicolare dal punto di applicazione e della forza applicata.
Può anche essere determinato risolvendo la forza nei suoi componenti e moltiplicando i singoli componenti con il braccio del momento corrispondente.
Si consideri una valvola in cui un volantino è montato su una tubazione. Quando viene applicata una forza per ruotare la ruota, il momento della forza attorno al centro può essere determinato moltiplicando l'entità della forza per la distanza perpendicolare dal centro al punto di applicazione.
La forza applicata può anche essere risolta nei suoi componenti e il momento può essere determinato sommando i prodotti di ciascun componente della forza con la distanza corrispondente.

<ol>
	<li>Hibbeler, R.C. (2016). Ingegneria Meccanica \u2012 Statica e Dinamica. Hoboken, New Jersey: Pearson Prentice Hall. pagine 132.</li>
</ol>

principio dei momenti

Il principio dei momenti, noto anche come teorema di Varignon, è un concetto fondamentale in fisica ed ingegneria che descrive l'equilibrio di un corpo rigido sotto l'influenza di forze esterne. Il principio afferma che il momento di una forza rispetto ad un punto è uguale alla somma dei momenti delle componenti della forza rispetto allo stesso punto.

Il momento viene calcolato moltiplicando la magnitudine della forza, per la distanza perpendicolare dal punto di applicazione, al punto rispetto al quale il momento viene calcolato. Considera una valvola dove una ruota a mano è montata su un condotto. Quando qualcuno applica una forza per girare la ruota, il momento della forza rispetto al centro può essere determinato moltiplicando la magnitudine della forza per la distanza perpendicolare dal centro al punto di applicazione della forza.

Tuttavia, il calcolo può diventare più complesso se la forza applicata non è perpendicolare alla valvola o ha più componenti. In questo caso, possiamo scomporre la forza nei suoi vettori componenti e calcolare individualmente il momento di ciascuna componente moltiplicandola per la distanza perpendicolare dal punto di applicazione di quella componente al punto rispetto al quale il momento viene calcolato. Una volta che ciascun momento è stato calcolato, possiamo sommarli per determinare il momento complessivo della forza rispetto al punto in questione.

Il principio dei momenti può essere utilizzato in una vasta gamma di applicazioni, dall'ingegneria strutturale alla progettazione meccanica. Calcolando i momenti delle forze che agiscono su un sistema o una struttura, possiamo determinare se è in equilibrio o se ruoterà o si muoverà a causa di un disequilibrio delle forze.

Principio dei Momenti

Il principio dei momenti, noto anche come teorema di Varignon, è un concetto fondamentale in fisica e ingegneria che descrive l'equilibrio di un ...

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JoVE Core

Mechanical Engineering

Ingegneria Meccanica

Unit 1

Unità 1

Force System Resultants

Risultanti dei sistemi di forze

KEY TERMS AND CONCEPTS

TERMINI E CONCETTI CHIAVE

Principle of Moments

resolving forces in moment calculations

The principle of moments, also called Varignon's theorem, explains how a force creates rotation about a point. It is a key idea in physics and engineering. It also helps describe when a rigid body stays in equilibrium under external forces.

The moment of a force is found by multiplying the force by the perpendicular distance from the point of application to the point being studied. A larger force or a larger distance gives a larger moment. This makes the idea useful for checking how strongly a force can turn an object.

A valve with a hand wheel on a pipeline gives a clear example. When a person pushes on the wheel, the moment about the center depends on the force and the perpendicular distance from the center to where the force is applied. If the force is not perpendicular to the valve, the calculation is less direct.

In that case, the force can be split into component vectors. Each component has its own moment, and each one is found using the perpendicular distance from the point of application of that component to the point of rotation. After the moments are found, they are added together to get the overall moment about the point.

This method is used in structural engineering and mechanical design. It helps show whether a system or structure is in equilibrium. It also shows when an imbalance of forces may cause rotation or motion.

Resolving Forces in Moment Calculations

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Net Moment Sign Convention in 2D Forces

Net moment in two-dimensional force systems shows how multiple forces can cause rotation about a fixed point. The scalar formulation helps analyze equilibrium in structures that are acted on by several forces. It focuses on the x-y plane and uses a simple sign rule to describe the direction of rotation. To find the resultant moment, the moments from all forces in the system are considered about a chosen point A. Each moment is assigned a sign based on its sense of rotation. Positive moments...

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Calculating Moment with Cartesian Vectors

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Resultant moment describes the total turning effect of multiple forces acting on an object. It shows how several forces can combine to make a body rotate about a point. In physics, moment is the tendency of a force to cause rotation. The resultant moment of a force system is a vector quantity. That means it can be added and subtracted like other vectors. For a system with two forces, F1 and F2, acting on a pole at points A and B, the resultant moment is written as MR = (rA x F1) + (rB x F2).

principle of moments

The principle of moments, also called Varignon's theorem, explains how a force creates rotation about a point. It is a key idea in physics and engineering. It also helps describe when a rigid body stays in equilibrium under external forces. The moment of a force is found by multiplying the force by the perpendicular distance from the point of application to the point being studied. A larger force or a larger distance gives a larger moment. This makes the idea useful for checking how strongly a...

principle of moments: problem solving

Torque About an Axis in 3D Systems

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Bicycle Torque and Moment About an Axis

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Torque on a Bicycle Wheel: Vector Method

Torque, or the moment of a force, explains how a force can make an object rotate about an axis. A bicycle is a clear example. When a cyclist presses on the pedal, the crankshaft turns and helps drive the wheel. To analyze this motion, a coordinate system is set up first. The x-axis is tangential to the wheel, the y-axis is perpendicular to the x-axis and points upward, and the z-axis points outward from the wheel. In this setup, the force on the wheel axle lies along the x-axis. The axle...

couple

Couple Moment in Force Systems

A couple is a pair of parallel forces that are equal in magnitude and opposite in direction. The two forces are separated by a perpendicular distance called the couple arm. Together, they create a turning effect on a body instead of a net push. This turning effect is called the couple moment. It rotates the body about an axis that is perpendicular to the plane of the forces. The SI unit for a couple moment is the Newton-meter (N-m). A common example is tightening a bolt with a lug wrench. In...

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Couple Moments and the Right-Hand Rule

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Equivalent Couples in Mechanical Systems

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Equivalent Force and Moment Systems

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Resultant Forces in Force and Couple Systems

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simplification of a force and couple system: ii

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Resultant Force and Wrench Motion

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Load distribution helps engineers describe how force spreads across a surface or structure. A distributed load is a continuous force per unit area, rather than a single point force. It is a common idea in many practical situations. A bookshelf full of stacked books is one simple example. The weight of the books is spread along the shelf, so the pressure changes across the surface. This pressure is measured in Newtons per square meter, or Pascals. A hydroelectric dam gives another clear...

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Structural engineering often requires finding the resultant load on a beam with changing force patterns. Here, a beam of length L carries a varying load made from parabolic and trapezoidal load distributions along the x-axis. The goal is to find the total load, where it acts, and the centroid of the combined area so the beam’s response can be predicted. The parabolic load is handled first. A small force element, dR, acts over a short distance, dx, and these elements are integrated across the...

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Equivalent Resultant Loads on Beams

Equivalent resultant loads on beams can be found by breaking a distributed load into smaller regions. This makes the beam easier to analyze. Each region can then be handled on its own before the results are combined. The magnitude of the equivalent resultant load for each region comes from the area of that region. In this setting, area represents the force applied by the distributed load over that part of the beam. After finding the force for each region, the position of each resultant load...

key terms and concepts

Learn how the principle of moments breaks a force into components and uses distance to find rotation in a valve, structure, or other rigid body.

Resolving Forces in Moment Calculations | 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.

mechanical engineering

Resolving Forces in Moment Calculations

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