How to calculate the moment of force F to Z axis
Publish: 2021-03-30 21:24:59
1. Take opening the door as an example
you pull the door outward
the door doesn't move
if you push harder, the door will fall off<
this is the meaning of the moment of force to the axis
to the fixed point
you can use the seesaw as an example
three children
two people sitting on the left and right sides
one child sitting in the middle
whether the children in the middle exist or not will not affect the children's game on both sides
in the middle
you pull the door outward
the door doesn't move
if you push harder, the door will fall off<
this is the meaning of the moment of force to the axis
to the fixed point
you can use the seesaw as an example
three children
two people sitting on the left and right sides
one child sitting in the middle
whether the children in the middle exist or not will not affect the children's game on both sides
in the middle
2. There are two cases when the moment of force to axis is zero: 1. The force is parallel to the axis; 2. The action line of force passes through the axis.
in fact, the moment of force to axis is the projection of the moment of force to any point on the axis on the axis
in fact, the moment of force to axis is the projection of the moment of force to any point on the axis on the axis
3. cosα＝1/(√1²+3²+5²)=0.169
同上
cosβ＝0.507 cos乄＝0.845
Fx=F×cosα=169N Fy=F×cosβ=507N
Mz=-Fx×(0.1+0.05)-Fy×0.15＝-101.4N.m
同上
cosβ＝0.507 cos乄＝0.845
Fx=F×cosα=169N Fy=F×cosβ=507N
Mz=-Fx×(0.1+0.05)-Fy×0.15＝-101.4N.m
4. First, the moment of the force P to point a is calculated, and the direction is along the Z axis, and then it is projected to ab; The projection of the moment of the force to the point on an axis passing through the point is equal to the moment of the force to the axis.
5. Your understanding of the right-hand rule is biased. The moment of force on the axis is r multiplied by F. the application method of the right-hand rule is: four fingers point to the direction of r first, then bend to the direction of F to make a fist (the direction of four fingers bending must point to the direction of F), and the direction of thumb along the axis is the direction of the moment.
if the palm direction changes (keep the four fingers pointing unchanged), the right-hand rule can be applied, Then, after the four fingers are clenched into fists, the four fingers can not point in the direction of F, but in the opposite direction of F, which is bound to draw a wrong conclusion. So your idea is wrong.
Question supplement:
I think I know your problem. When studying the torque, the axis, R, and F are perpendicular to each other. The axis is the direction of the torque, and R is the arm of force perpendicular to the axis and F, which is a vector, The direction is from the axis to F. f must take the component force perpendicular to the axis. The moment of the component force parallel to the axis to the axis is 0, and this component force is not considered when studying the moment.
in your example, the direction of R is not from O to the point of action of the force, but from X to the point of action of F, and is perpendicular to both X and F. in this way, you can determine the moment of F to X, Of course, if the thumb is the same as the X axis, it is positive, otherwise it is negative
if the palm direction changes (keep the four fingers pointing unchanged), the right-hand rule can be applied, Then, after the four fingers are clenched into fists, the four fingers can not point in the direction of F, but in the opposite direction of F, which is bound to draw a wrong conclusion. So your idea is wrong.
Question supplement:
I think I know your problem. When studying the torque, the axis, R, and F are perpendicular to each other. The axis is the direction of the torque, and R is the arm of force perpendicular to the axis and F, which is a vector, The direction is from the axis to F. f must take the component force perpendicular to the axis. The moment of the component force parallel to the axis to the axis is 0, and this component force is not considered when studying the moment.
in your example, the direction of R is not from O to the point of action of the force, but from X to the point of action of F, and is perpendicular to both X and F. in this way, you can determine the moment of F to X, Of course, if the thumb is the same as the X axis, it is positive, otherwise it is negative
6. Your understanding of the right hand rule is biased. The moment of the force on the axis is r cross multiplied by F. the application method of the right hand rule is: four fingers first point to the direction of R, and then bend to the direction of F to make a fist (the bending direction of the four fingers must point to the direction of F), and the direction of the thumb along the axis is the direction of the moment
if the palm direction changes (keep the four fingers pointing to the same direction), then after the four fingers are clenched into a fist, the four fingers can not point to the direction of F, but to the opposite direction of F, which is bound to draw a wrong conclusion. So your idea is wrong
question add:
I think I know what your problem is. When studying the moment, the axis, R, and F are perpendicular to each other. The axis is the direction of the moment, and R is the arm of force perpendicular to the axis and F. it is a vector and the direction is from the axis to F. F must be a component perpendicular to the axis. The moment of the component parallel to the axis to the axis is 0, which is not considered in the study of moment
in your example, the direction of R is not from O to the point of action of the force, but from the x-axis to the point of action of F, and is perpendicular to both the x-axis and F. So you can tell that the moment of F on the x-axis must be along the axis. Of course, if the thumb is the same as the X axis, it is positive, otherwise it is negative.
if the palm direction changes (keep the four fingers pointing to the same direction), then after the four fingers are clenched into a fist, the four fingers can not point to the direction of F, but to the opposite direction of F, which is bound to draw a wrong conclusion. So your idea is wrong
question add:
I think I know what your problem is. When studying the moment, the axis, R, and F are perpendicular to each other. The axis is the direction of the moment, and R is the arm of force perpendicular to the axis and F. it is a vector and the direction is from the axis to F. F must be a component perpendicular to the axis. The moment of the component parallel to the axis to the axis is 0, which is not considered in the study of moment
in your example, the direction of R is not from O to the point of action of the force, but from the x-axis to the point of action of F, and is perpendicular to both the x-axis and F. So you can tell that the moment of F on the x-axis must be along the axis. Of course, if the thumb is the same as the X axis, it is positive, otherwise it is negative.
7. A moment is a vector. The direction of the moment on the z-axis is the same as that of the z-axis. The projection perpendicular to the z-axis refers to the projection of the force, and the projection of the z-axis refers to the projection of the moment on the z-axis
8. Just look at the direction that the component forces make the object rotate around the moment center. If it is counterclockwise, it is positive, and clockwise is negative
9. The direction of the moment is determined by the vector algorithm, that is, when the bending direction of the four fingers of the right hand turns from the displacement direction along the angle direction less than 180 degrees to the force vector, the direction of the thumb is positive if it is the same as the assumed positive direction, otherwise it is negative
in practice, it is troublesome to do so. We can see from the assumed positive direction. If the force causes the object to rotate counterclockwise, we will record the moment of the force as positive, otherwise it will be negative
force is the translation of a point. Of course, the line and surface can be driven by the point. The moment is composed of two actual forces (reference system), and the moment is the rotation of a line. Let's assume that all forces are 1 Newton forces acting on a point. How do you distinguish them? The answer is direction. These directions form a ball in the three-dimensional world. Similarly, suppose that the torque of 1 nm acts on a straight line. How do you distinguish them? The answer is also direction. Different torques have different directions of rotation. Each direction of rotation determines a plane. For a straight line, if you insert a normal at any point on it, its rotation will be unique. That is to say, a line can distinguish torques in different directions, so the normal of the plane of rotation is the direction of the torque. As for clockwise and counterclockwise, Just like the force forward and backward, it's opposite, so it's positive and negative. The dimension of moment is distance × power; The same dimension as energy. But the moment is usually in Newton meters, not joules. The unit of moment is determined by the unit of force and arm of force. A physical quantity in which a force turns a body. It can be divided into moment of force to axis and moment of force to point. The moment of a force on an axis is the physical quantity of a force on an object rotating around an axis. It is an algebraic quantity whose magnitude is equal to the proct of the component of the force in the plane perpendicular to the axis and the vertical distance from the line of action of the component to the axis; The sign is used to distinguish the different turns of torque. It is determined according to the right hand screw rule: clench the fist with the four fingers of the right hand along the component direction (x axis / Y axis) and the palm facing the rotation axis (x axis / Y axis), and take the positive sign when the thumb direction (Z axis) is consistent with the positive direction of the axis, otherwise take the negative sign. The moment of a force to a point is the physical quantity that the force rotates the object around a certain point. It is a vector, which is equal to the vector proct of the position vector r of the force acting point and the force vector F. For example, an object fixed at point o with a spherical hinge is subjected to a force F. R is used to represent the position vector from point O to point a, and the angle between R and F is a (see Figure). Under the action of F, the object rotates around the plane perpendicular to R and F and through the axis of o point. The magnitude of rotation and the direction of rotation axis depend on the moment vector m of F to o point, M = R × F The size of M is rfsina and the direction is determined by the right hand rule. The projection of moment M on the rectangular coordinate axis passing through the moment center O is MX, my and MZ. It can be proved that MX, my and MZ are the moments of F on the X, y and Z axes. The dimension of moment is l2mt - 2, and its international unit is n · M. For example, the moment of 3 Newton force acting on the lever 2 meters away from the fulcrum is equal to the moment of 1 Newton force acting on the lever 6 meters away from the fulcrum. Here, it is assumed that the force is perpendicular to the lever. In general, the moment can be defined as the cross proct of vectors (Note: not the vector dot proct): where R is the vector from the axis of rotation to the force and F is the vector force.
in practice, it is troublesome to do so. We can see from the assumed positive direction. If the force causes the object to rotate counterclockwise, we will record the moment of the force as positive, otherwise it will be negative
force is the translation of a point. Of course, the line and surface can be driven by the point. The moment is composed of two actual forces (reference system), and the moment is the rotation of a line. Let's assume that all forces are 1 Newton forces acting on a point. How do you distinguish them? The answer is direction. These directions form a ball in the three-dimensional world. Similarly, suppose that the torque of 1 nm acts on a straight line. How do you distinguish them? The answer is also direction. Different torques have different directions of rotation. Each direction of rotation determines a plane. For a straight line, if you insert a normal at any point on it, its rotation will be unique. That is to say, a line can distinguish torques in different directions, so the normal of the plane of rotation is the direction of the torque. As for clockwise and counterclockwise, Just like the force forward and backward, it's opposite, so it's positive and negative. The dimension of moment is distance × power; The same dimension as energy. But the moment is usually in Newton meters, not joules. The unit of moment is determined by the unit of force and arm of force. A physical quantity in which a force turns a body. It can be divided into moment of force to axis and moment of force to point. The moment of a force on an axis is the physical quantity of a force on an object rotating around an axis. It is an algebraic quantity whose magnitude is equal to the proct of the component of the force in the plane perpendicular to the axis and the vertical distance from the line of action of the component to the axis; The sign is used to distinguish the different turns of torque. It is determined according to the right hand screw rule: clench the fist with the four fingers of the right hand along the component direction (x axis / Y axis) and the palm facing the rotation axis (x axis / Y axis), and take the positive sign when the thumb direction (Z axis) is consistent with the positive direction of the axis, otherwise take the negative sign. The moment of a force to a point is the physical quantity that the force rotates the object around a certain point. It is a vector, which is equal to the vector proct of the position vector r of the force acting point and the force vector F. For example, an object fixed at point o with a spherical hinge is subjected to a force F. R is used to represent the position vector from point O to point a, and the angle between R and F is a (see Figure). Under the action of F, the object rotates around the plane perpendicular to R and F and through the axis of o point. The magnitude of rotation and the direction of rotation axis depend on the moment vector m of F to o point, M = R × F The size of M is rfsina and the direction is determined by the right hand rule. The projection of moment M on the rectangular coordinate axis passing through the moment center O is MX, my and MZ. It can be proved that MX, my and MZ are the moments of F on the X, y and Z axes. The dimension of moment is l2mt - 2, and its international unit is n · M. For example, the moment of 3 Newton force acting on the lever 2 meters away from the fulcrum is equal to the moment of 1 Newton force acting on the lever 6 meters away from the fulcrum. Here, it is assumed that the force is perpendicular to the lever. In general, the moment can be defined as the cross proct of vectors (Note: not the vector dot proct): where R is the vector from the axis of rotation to the force and F is the vector force.
Hot content