“moment(in mechanics)”的概念、定义、翻译、参考文献-科学参考

moment(in mechanics)

Mathematics

A means of describing the turning effect of a force about a point. For a system of coplanar forces, the moment of one of the forces F about any point A in the plane can be defined as the product of the magnitude of F and the distance from A to the line of action of F and is considered to be acting either clockwise or anticlockwise. For example, suppose that forces with magnitudes F₁ and F₂ act at B and C, as shown in the figure. The moment of the first force about A is F₁d₁ clockwise, and the moment of the second force about A is F₂d₂ anticlockwise. The principle of moments considers when a system of coplanar forces produces a state of equilibrium.

Moments about A

However, a better approach is to define the moment of the force F, acting at a point B, about the point A as the vector (r_B−r_A) × F, where × denotes the vector product and r_A, r_B are the position vectors of A and B. The use of vectors not only eliminates the need to distinguish between clockwise and anticlockwise directions but facilitates the measuring of the turning effects of non‐coplanar forces acting on a 3‐dimensional body.

Similarly, for a particle P with position vector r and linear momentum p, the moment of the linear momentum of P about the point A is the vector (r−r_A) × p. This is the angular momentum of the particle P about the point A.

Suppose that a couple consists of a force F acting at B and a force −F acting at C. The moment of the couple about A is equal to

$(r_{B} - r_{A}) \times F + (r_{C} - r_{A}) \times (- F) = (r_{B} - r_{C}) \times F,$

which is independent of the position of A.

单词	moment(in mechanics)
释义	moment(in mechanics) Mathematics A means of describing the turning effect of a force about a point. For a system of coplanar forces, the moment of one of the forces F about any point A in the plane can be defined as the product of the magnitude of F and the distance from A to the line of action of F and is considered to be acting either clockwise or anticlockwise. For example, suppose that forces with magnitudes F₁ and F₂ act at B and C, as shown in the figure. The moment of the first force about A is F₁d₁ clockwise, and the moment of the second force about A is F₂d₂ anticlockwise. The principle of moments considers when a system of coplanar forces produces a state of equilibrium. Moments about A However, a better approach is to define the moment of the force F, acting at a point B, about the point A as the vector (r_B−r_A) × F, where × denotes the vector product and r_A, r_B are the position vectors of A and B. The use of vectors not only eliminates the need to distinguish between clockwise and anticlockwise directions but facilitates the measuring of the turning effects of non‐coplanar forces acting on a 3‐dimensional body. Similarly, for a particle P with position vector r and linear momentum p, the moment of the linear momentum of P about the point A is the vector (r−r_A) × p. This is the angular momentum of the particle P about the point A. Suppose that a couple consists of a force F acting at B and a force −F acting at C. The moment of the couple about A is equal to $(r_{B} - r_{A}) \times F + (r_{C} - r_{A}) \times (- F) = (r_{B} - r_{C}) \times F,$ which is independent of the position of A.
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