Name: bicycle torque and moment about an axis
Uploaded: 2023-09-22T11:49:21.000Z
Duration: 1 min 28 s
Channel: JoVE

ضع في اعتبارك راكب دراجة يركب دراجة ويمارس القوة على الدواسة لتدوير العجلة. عندما تمارس قوة على الدواسة ، تمارس السلسلة المرفقة قوة على تروس العجلة. تدور العجلة حول محورها ، لذلك يمر محور الدوران من خلالها.
تقيس لحظة القوة على طول المحور مقدار القوة التي تتسبب في دوران الجسم حول نقطة أو محور معين.
في هذه الحالة ، تدور العجلة حول المحور y في المستوى xz. هنا ، ذراع اللحظة أو المسافة العمودية بين محور الدوران وخط عمل القوة هي نصف قطر التروس.
إذن، عزم القوة حول المحور y يساوي فرسينθ.
بما أن القوة عرضية، فإن الزاوية بين متجه القوة ونصف القطر تساوي 90 درجة.
في الدراجة ، يمكن ضرب لحظة القوة في السرعة الزاوية للمحور للحصول على الطاقة الناتجة عن دوران العجلة.

<ol>
	<li>هيبلر ، آر سي (2016). الميكانيكا الهندسية - الإحصاء والديناميكيات. هوبوكين ، نيو جيرسي: قاعة بيرسون برنتيس. ص 145.</li>
</ol>

المفهوم القياسي لعزم القوة حول محور.

Moment of a Force About an Axis: Scalar

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عزم القوة حول محور معين هو مفهوم أساسي في علم الميكانيكا يساعد في تحديد الحركة الدورانية لجسم حول نقطة أو محور محدد. يمكن حساب عزم القوة باستخدام التحليل القياسي، والذي يتضمن أخذ المسافة العمودية بين محور الدوران وخط تأثير القوة، هذه المسافة تعرف باسم ذراع العزم

لاستيعاب مفهوم عزم القوة بشكل أفضل، دعونا نأخذ مثالاً لراكب دراجة هوائية. عندما يضغط الراكب على الدواسة، فإن السلسلة المتصلة تنقل القوة إلى محور العجلة، مما يؤدي إلى دورانها. في هذه الحالة، يمر محور الدوران عبر محور العجلة، بينما يكون ذراع العزم هو نصف قطر محور العجلة . وعليه، فإن عزم القوة حول محور الدوران يُعطى بالمعادلة التالية:

<img alt="Equation 1" src="/files/ftp_upload/14258/14258_Equation_1v2.svg" style="text-align: center; height: 13px;" />

حيث، F هي القوة المطبقة، r هي نصف قطر محور العجلة، و θ هي زاوية بين متجه القوة والنصف قطر. نظرًا لأن القوة المطبقة تكون مماسية، فإن الزاوية بين متجه القوة ونصف القطر تساوي 90 درجة.

في الدراجة الهوائية، يمكن ضرب عزم القوة في السرعة الزاوية للمحور للحصول على القدرة الناتجة عن دوران العجلة. يُعد عزم القوة عاملاً أساسيًا في تصميم مختلف الهياكل والآلات، بما في ذلك الدراجات الهوائية، والسيارات، والطائرات، لضمان استقرارها وسلامتها.
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لحظة القوة حول المحور هي مفهوم حاسم في الميكانيكا يساعد في تحديد الحركة الدورانية للجسم حول نقطة معينة أو ...

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Mechanical Engineering

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Unit 1

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Force System Resultants

محصلات نظام القوى

KEY TERMS AND CONCEPTS

المصطلحات والمفاهيم الأساسية

bicycle torque and moment about an axis

The moment of a force about an axis describes how a force can make an object turn around a fixed line. In scalar analysis, the moment is found from the perpendicular distance between the axis of rotation and the line of action of the force. That distance is called the moment arm.

A bicycle gives a clear example of this idea. When the cyclist pushes on the pedal, the chain applies a force to the wheel’s axle and makes it rotate. The axis of rotation passes through the axle, and the moment arm is the axle radius.

For this case, the moment of force about the axis depends on the force, the radius, and the angle between the force vector and the radius. Because the force is tangential, that angle is 90 degrees. The moment of force can also be multiplied by the angular velocity of the axle to find the power produced by the wheel rotation.

This concept is important in the design of bicycles, automobiles, and aircraft. Engineers use it to help maintain stability and safety in these machines and structures.

Bicycle Torque and Moment About an Axis

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Torque on a Flywheel: Direction and Size

Torque, or the moment of a force, describes how a force can make an object turn about an axis. It is a vector quantity, so it has both size and direction. This idea is important in physics, mechanics, and engineering. A simple flywheel example shows how torque works. The flywheel rotates about point O when a force is applied to it. The moment arm is the perpendicular distance from point O to the line of action of the force. The moment, in newton-meter (N-m), is found by multiplying the force...

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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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The moment of force describes the twisting effect a force can have on an object. It shows why a force may cause rotation instead of straight-line motion. The moment arm is the perpendicular distance from the force’s line of action to the axis of rotation. The moment of force is a vector quantity, not a scalar. Its vector form comes from the cross product of the position vector and the force vector. A cross product gives a vector that is perpendicular to both input vectors. The moment about a...

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Calculating moment with Cartesian vectors shows how position and force vectors work together. The moment of force is the cross product of these vectors, so it is a vector quantity. In Cartesian form, unit vectors help write the vectors in component form. The cross product can be arranged in determinant form. That determinant is then expanded to find the Cartesian vector form of the moment of force. This method gives a clear way to work through the calculation step by step. A revolving door...

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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

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...

principle of moments: problem solving

Torque About an Axis in 3D Systems

The principle of moments helps solve torque problems in physics and engineering. It describes how forces and moments balance around a pivot point or axis. It is used in many real-life cases, including construction, sports, and everyday actions like opening doors and pushing objects. The problem here uses a pole in a three-dimensional system with a cable attached. When tension acts in the cable, the goal is to find the moment about the z-axis through the base. One method is to project the force...

moment of a force about an axis: scalar

The moment of a force about an axis describes how a force can make an object turn around a fixed line. In scalar analysis, the moment is found from the perpendicular distance between the axis of rotation and the line of action of the force. That distance is called the moment arm. A bicycle gives a clear example of this idea. When the cyclist pushes on the pedal, the chain applies a force to the wheel’s axle and makes it rotate. The axis of rotation passes through the axle, and the moment arm...

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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...

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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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Structural systems often experience several forces and couple moments at the same time. Engineers simplify these loading cases by replacing them with an equivalent force and moment system at a chosen point O. This makes the analysis easier while keeping the same external effects on the member. A key idea in this process is the principle of transmissibility. A force is a sliding vector, which means it can be moved anywhere along its line of action without changing how the body behaves...

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Resultant Forces in Force and Couple Systems

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key terms and concepts

Learn how the moment of a force about an axis is found with scalar analysis, using a bicycle axle example and its link to rotational power.

Bicycle Torque and Moment About an Axis | 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

Bicycle Torque and Moment About an Axis

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