Is the principal moment a force
formal
See which direction of the original force at o point, determine the direction of the torque, clockwise torque is negative, anticlockwise torque is positive, and then sum the partial torque, the main torque is obtained
The basic measure of mechanical interaction between objects is force, and the concepts of moment of force to point and moment of force to axis are widely used in theoretical mechanicsthe change of the motion of the object is not only related to the force, but also related to its own inertia. For a particle, the measure of inertia is its mass. For a rigid body, in addition to its total mass, the inertia is also related to the distribution of mass in the body, that is, the position of the center of mass, the moment of inertia and the proct of inertia. The moment of inertia and the proct of inertia of a rigid body to three mutually perpendicular coordinate axes constitute the inertia tensor of the rigid body to the coordinate system
In dynamics, the measurement of motion includes momentum, moment of momentum and kinetic energy, and the measurement of force action includes impulse, moment of impulse and work. The theorems that show the relationship between these two measures include the theorem of momentum, the theorem of moment of momentum and the theorem of kinetic energy, which are called the general theorem of dynamics
< H2 > extended data: theoretical mechanics is based on Newton's three laws: the first law is the law of inertia; The second law gives the basic equations of particle dynamics; The third law, that is, the law of action and reaction, plays an important role in the study of mechanical problems of particle system. The first and second laws hold for inertial reference frame
in general problems, the reference frame that consolidates with the earth or makes inertial motion relative to the ground can be regarded as inertial reference frame approximately
the more effective method to study the equilibrium and motion of non free particle system is the variational principle of mechanics, including virtual displacement principle, D'Alembert principle, Hamiltonian principle and so on. The derived differential equations of motion are widely used in solving problems, including Lagrange equation, Hamiltonian canonical equation, Hamiltonian Jacobian equation and so on
the principal vector determines the translational acceleration of the force system, and the principal moment determines the rotational acceleration of the force system
the principal moment M and the principal vector r are the results of simplifying the force system to the simplified center, and they are both vectors
the resultant force and the resultant couple are the results of the final simplification of the force system, and both are vectors
for example, if R and m are vertical after simplification to the simplification center a, further simplification can be made.
The principal moment of a plane general force system is related to the position of the simplified center! As shown in the figure, if each force is simplified to point a, the moment of each force to point a is counterclockwise; If each force is simplified to point B, the moment of each force to point B is clockwise. I just studied the direction, but not the size
four fingers bend along the rotation direction, the straight thumb finger represents the rotation axis,
if the thumb finger points out of the book, or the thumb finger points to the positive direction of the rotation axis,
then the torque turns counterclockwise and the sign is positive< On the contrary, the moment turns clockwise and the sign is negative.
after simplifying a and B, the main moment is zero, the main loss is not zero, and a and B pass through the main loss
it can't be a couple
if it is a couple, it will be a couple after any point is simplified, which is inconsistent with the title conditions
maybe it's equilibrium.
for points a and B, if the simplified principal moment is zero and the principal loss is zero, then it's equilibrium
2. Equilibrium
suppose a, B and C. It is known that the principal moment is zero for point A. if the principal moment is also zero, it must be balanced; If the main loss is not zero, the main loss must pass point a
simplify the main moment (at this time, the main moment is zero) to B and C, because a, B and C are not collinear, so there must be a non-zero main moment for B and C, which is contradictory to the topic and the hypothesis is not tenable. Therefore, this force system is a balance force system
3. No
suppose that the earth revolves around the sun, only revolves around the sun, and does not rotate (only hypothesis). At this time, every point on the earth is doing circular motion, but this is not called fixed axis rotation, this is called translation (parallel movement).
as long as the resultant force (the extension line of the resultant force) does not pass through the center of mass, the resultant force will proce a moment to the rigid body. Only when the resultant force is translated to the center of mass can the moment be eliminated. The force system is further simplified.
no
no