- #1
DiamondV
- 103
- 0
I'm confused about point 2. It says V=PQsintheta. How is that formula derived?
Solving Torque & Moment: Deriving V=PQsintheta
In summary, the "formula" V = PQ sin(theta) is part of the definition of a cross product and is not "derived".
I'm confused about point 2. It says V=PQsintheta. How is that formula derived?
- #2
DrPapper
- 48
- 9
Hello DiamondV
If you've taken multi-variable calculus you may recall something known as the Vector Cross Product. The magnitude of V can be thought of as how perpendicular the two vectors that produce it are to each other. So if you had P and Q directly on top of each other the "magnitude" of their "perpendicular-ness" would be zero. But if they are completely perpendicular then $$Sin \theta = 1$$ when $$\theta = \pi / 2$$ so it's the regular multiplication of P and Q. A mathematician could give you a more proper answer I'm sure. Check your Calculus textbook under the section of vector cross product.
Hope that helps.
If you've taken multi-variable calculus you may recall something known as the Vector Cross Product. The magnitude of V can be thought of as how perpendicular the two vectors that produce it are to each other. So if you had P and Q directly on top of each other the "magnitude" of their "perpendicular-ness" would be zero. But if they are completely perpendicular then $$Sin \theta = 1$$ when $$\theta = \pi / 2$$ so it's the regular multiplication of P and Q. A mathematician could give you a more proper answer I'm sure. Check your Calculus textbook under the section of vector cross product.
Hope that helps.
- #3
IgorIGP
- 52
- 2
Imho, the phrase:
Moreover, I believe that the one of the ways to understand the cross product is a moment of force concept. That is the moment of force is a good illustration of the vector product that shows its physical sense from the point of view of one of the branches of mechanics.
The world is so constituted that sometimes the things depend on the result of a pair of vector quantities. This is well illustrated by calculating the area of a parallelogram in the course of geometry. In mechanics, the moment of a force is a good example. The power of rotated force is defined by that. Imagine a solid flat body fixed at the point O to rotate in its plane. Suppose there is a pair of forces F1 and F2 applied at the points M1 and M2, respectively. Let the forces F1 and F2 are directed so that they try to turn the body in opposite directions. Let the forces F1 and F2 are perpendicular OM1 and OM2 respectively. Equality of works of these forces in the infinitely small arcs of movement is a condition of equilibrium of the body. The arc of each force is the product of its radius (OM1 and OM2 respectively) an infinitesimal angle. The angles of both are equal but not equal to zero, so they can be cut. This means that the determining factor in the rotation moving is not the force but it is product of of the force and its radius. And that can be a good illustration to a such abstract concept as a vector product.
is a fantasy humanities.DiamondV said:
Moreover, I believe that the one of the ways to understand the cross product is a moment of force concept. That is the moment of force is a good illustration of the vector product that shows its physical sense from the point of view of one of the branches of mechanics.
The world is so constituted that sometimes the things depend on the result of a pair of vector quantities. This is well illustrated by calculating the area of a parallelogram in the course of geometry. In mechanics, the moment of a force is a good example. The power of rotated force is defined by that. Imagine a solid flat body fixed at the point O to rotate in its plane. Suppose there is a pair of forces F1 and F2 applied at the points M1 and M2, respectively. Let the forces F1 and F2 are directed so that they try to turn the body in opposite directions. Let the forces F1 and F2 are perpendicular OM1 and OM2 respectively. Equality of works of these forces in the infinitely small arcs of movement is a condition of equilibrium of the body. The arc of each force is the product of its radius (OM1 and OM2 respectively) an infinitesimal angle. The angles of both are equal but not equal to zero, so they can be cut. This means that the determining factor in the rotation moving is not the force but it is product of of the force and its radius. And that can be a good illustration to a such abstract concept as a vector product.
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- #4
Chandra Prayaga
Science Advisor
- 652
- 150
The "formula" V = PQ sin(theta) is not "derived". It is part of the definition of a cross product.
- #5
IgorIGP
- 52
- 2
I absolutely agree with you. Who can explain me on how to measure the vector of the force moment that "line of action is perpendicular to plane" were the force and its radius (do not know how is named on english this line segment) act? The analogy where the moment of force derives from the cross product is bad. Softly said.Chandra Prayaga said:
The concepts of mathematics can derive from the concepts of the real world, but not vice versa. And in this case, as the parent concept it is better to choose something from the electrodynamics like Lorentz force ie (imho).
What is torque and moment?
Torque is the measure of the force that can cause an object to rotate around an axis. It is calculated by multiplying the force applied to the object by the distance from the axis of rotation. Moment is a specific type of torque that is applied at a particular point on an object and is used to measure the tendency of the object to rotate around that point.
How do you calculate torque and moment?
Torque is calculated by multiplying the force applied to an object by the distance from the axis of rotation. Moment is calculated by multiplying the force applied to an object by the perpendicular distance from the point of rotation to the line of action of the force. The formula for calculating torque is torque = force x distance and the formula for calculating moment is moment = force x distance x sin(theta).
What is the relationship between torque, moment, and power?
Torque and moment are both measures of force and their relationship is that torque is a general term for the force that causes an object to rotate, while moment is a specific type of torque that is applied at a particular point on an object. Power, on the other hand, is the rate at which work is done or energy is transferred. In the equation P=Q/t, where P is power, Q is work, and t is time, torque and moment are both involved in the calculation of work.
What is the significance of sin(theta) in the formula for calculating moment?
The sin(theta) in the formula for calculating moment represents the angle between the force applied to an object and the distance from the point of rotation to the line of action of the force. This angle is important because it determines the direction and magnitude of the moment. If the angle is 90 degrees (sin(90)=1), the moment will be at its maximum. If the angle is 0 degrees (sin(0)=0), there will be no moment generated.
What are some real-world applications of torque and moment?
Torque and moment are used in many real-world applications, such as in engineering and construction to calculate the strength and stability of structures. They are also important in the design and operation of machines, such as engines and motors. In sports, torque and moment are crucial in activities like throwing a ball or swinging a golf club. In physics, they are used to understand the rotational motion of objects and to explain phenomena like angular momentum and rotation around an axis.
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