Name: torque about an axis in 3d systems
Uploaded: 2023-09-22T11:49:21.000Z
Duration: 1 min 30 s
Channel: JoVE

Consider a pole placed in a 3-dimensional system with a cable attached. When the tension of 15 kN is applied to the cable, determine the moment about the z-axis passing through the base.
The moment can be determined using two methods.
In the first method, calculate the projection of the force along the unit vector and multiply it by the force&#39;s magnitude to obtain the force vector.
The moment about the origin is the cross-product of the position vector and the force. The moment along the z-axis can be obtained by the dot product of the moment about the origin and the unit vector along the z-axis.
Alternatively, resolve the force vector into its components. The components along the y-axis and z-axis exert no moment as they pass through and are parallel to the z-axis, respectively.
The tension in the x-direction can be obtained by multiplying the tension with the direction cosine with respect to the x-axis.
Recall the moment of force equation, and by substituting the terms, the moment about the z-axis can be determined.

principle of moments: problem solving

The principle of moments is a fundamental concept in physics and engineering. It refers to the balancing of forces and moments around a point or axis, also known as the pivot. This principle is used in many real-life scenarios, including construction, sports, and daily activities like opening doors and pushing objects.
One such scenario involves a pole placed in a three-dimensional system with a cable attached. When a tension is applied to the cable, the moment about the z-axis passing through the base needs to be determined. There are two methods to approach this problem.
The first method involves calculating the projection of the force along the unit vector and multiplying it by the force&#39;s magnitude to obtain the force vector. The moment about the origin can be calculated by taking the cross-product of the position vector and the force vector. Once the moment vector is determined, the moment along the z-axis can be evaluated by taking the dot product of the moment about the origin and the unit vector along the z-axis.
Alternatively, resolve the force vector into its components. The components along the y-axis and z-axis exert no moment as they pass through and are parallel to the z-axis, respectively. The tension in the x-direction can be calculated by multiplying the tension with the direction cosine with respect to the x-axis. Then, use the moment of force equation and substitute the appropriate terms to determine the moment about the z-axis.
It is important to note that the principle of moments is crucial in understanding the behavior of structures and machines. Engineers and designers use it extensively to ensure their creations are stable, safe, and effective. By balancing the forces and moments around a pivot point, they can calculate the stresses and strains that a structure or machine will endure and identify potential failure points.
Overall, the principle of moments is a powerful tool that helps to solve problems related to forces, torques, and motion. Whether it is regarding building bridges, analyzing sports techniques, or simply opening a door, one can rely on this principle to ensure that things are done correctly and efficiently.

Principle of Moments: Problem Solving

The principle of moments is a fundamental concept in physics and engineering. It refers to the balancing of forces and moments around a point or axis, ...

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Force System Resultants

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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 along a unit vector to build the force vector. The moment about the origin is then found with the cross product of the position vector and the force vector. After that, the moment along the z-axis is found by taking the dot product of the moment vector with the z-axis unit vector.

A second method is to split the force into components. The y-axis and z-axis components create no moment in this setup. The y-axis component passes through the axis, and the z-axis component is parallel to it. The x-direction tension is found by multiplying the cable tension by the direction cosine with respect to the x-axis. Then the moment of force equation is used to determine the moment about the z-axis.

This kind of analysis is important in structures and machines. Engineers and designers use the principle of moments to check stability, safety, and performance. It helps them estimate the stresses and strains a structure or machine may face and spot possible failure points. The same idea also appears in bridges, sports technique, and simple tasks like opening a door.

Torque About an Axis in 3D Systems

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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...

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key terms and concepts

Learn how the principle of moments is used to find torque about the z-axis in a 3D cable-and-pole setup using cross products and force components.

Torque About an Axis in 3D Systems | JoVE K12

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Torque About an Axis in 3D Systems

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