Simple argument that a force applied farther from the rotation axis

Thread starter aaaa202
Start date Aug 20, 2012
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Applied Argument Axis Force Force applied Rotation

In summary, torque is a measure of how a force applied at a distance from the rotation axis can cause a body to rotate. This is because the force is transmitted through the body, causing an imbalance in the forces and resulting in rotational acceleration. While energy considerations can explain the rotation once it has started, it cannot explain why the body starts to rotate in the first place. This is where the concept of torque, and the fact that a force applied at a greater distance has a greater tendency to rotate the body, comes into play. This can be observed in experiments, but cannot be proven mathematically without taking into account the effects of inertia.

Aug 22, 2012

Aimless

aaaa202 said:

I think this is exactly the type of argument I have been looking for. It will take me some time to get into your way of thinking though. Is the picture you describe similar to the one I have tried to draw on the attached sketch?

Yes; that's about what I was trying to describe. This view of things is oversimplified, but at a qualitative level I think it captures the dynamics of how internal stresses on a microscopic level can translate into rotation on a macroscopic level.

From a teaching perspective, it might be worth it to construct a numerical simulation of a model along these lines (with tunable string constants) and allowing it to evolve in time. It shouldn't be all that difficult; certainly nothing compared to, say, a DFT calculation.

<h2>What is a simple argument for why a force applied farther from the rotation axis produces a greater torque?</h2><p>The simple argument is based on the concept of leverage. When a force is applied at a greater distance from the rotation axis, it creates a longer lever arm, which increases the torque produced. This can be seen by comparing the equations for torque (T = F x d) and moment of inertia (I = mr^2), where the distance from the rotation axis (r) is squared in the moment of inertia equation.</p><h2>How does the direction of the force affect the torque produced?</h2><p>The direction of the force is important in determining the direction of the torque produced. If the force is applied perpendicular to the lever arm, it will produce the maximum torque. If the force is applied at an angle, the torque produced will be less than the maximum, with the exact amount depending on the angle between the force and the lever arm.</p><h2>What is the relationship between the magnitude of the force and the torque produced?</h2><p>The magnitude of the force and the torque produced are directly proportional. This means that as the force increases, the torque produced will also increase, assuming the distance from the rotation axis remains constant.</p><h2>How does the mass of the object being rotated affect the torque produced?</h2><p>The mass of the object being rotated is a factor in determining the torque produced, as it affects the moment of inertia. Objects with a greater mass will have a greater moment of inertia, meaning that a greater force or a longer lever arm will be needed to produce the same amount of torque as a lighter object.</p><h2>What are some practical applications of understanding the relationship between force, distance, and torque?</h2><p>Understanding the relationship between force, distance, and torque is important in many fields, including engineering, physics, and sports. It can be used to design more efficient machines, such as bicycles and cars, and to calculate the necessary force and distance for a given torque. In sports, it can help athletes optimize their movements to produce the maximum amount of torque, such as in swinging a golf club or throwing a discus.</p>

Related to Simple argument that a force applied farther from the rotation axis

What is a simple argument for why a force applied farther from the rotation axis produces a greater torque?

The simple argument is based on the concept of leverage. When a force is applied at a greater distance from the rotation axis, it creates a longer lever arm, which increases the torque produced. This can be seen by comparing the equations for torque (T = F x d) and moment of inertia (I = mr^2), where the distance from the rotation axis (r) is squared in the moment of inertia equation.

How does the direction of the force affect the torque produced?

The direction of the force is important in determining the direction of the torque produced. If the force is applied perpendicular to the lever arm, it will produce the maximum torque. If the force is applied at an angle, the torque produced will be less than the maximum, with the exact amount depending on the angle between the force and the lever arm.

What is the relationship between the magnitude of the force and the torque produced?

The magnitude of the force and the torque produced are directly proportional. This means that as the force increases, the torque produced will also increase, assuming the distance from the rotation axis remains constant.

How does the mass of the object being rotated affect the torque produced?

The mass of the object being rotated is a factor in determining the torque produced, as it affects the moment of inertia. Objects with a greater mass will have a greater moment of inertia, meaning that a greater force or a longer lever arm will be needed to produce the same amount of torque as a lighter object.

What are some practical applications of understanding the relationship between force, distance, and torque?

Understanding the relationship between force, distance, and torque is important in many fields, including engineering, physics, and sports. It can be used to design more efficient machines, such as bicycles and cars, and to calculate the necessary force and distance for a given torque. In sports, it can help athletes optimize their movements to produce the maximum amount of torque, such as in swinging a golf club or throwing a discus.