How to calculate the electric field force moment
The moment of force is the physical quantity of the rotation of an object. It can be divided into moment of force to axis and moment of force to point. That is: M = lxf. Where l is the distance vector from the axis of rotation to the point of force and F is the vector force; The moment is also a vector
the moment of a force on an axis is the physical quantity that the force acts on an object to rotate about an axis, and its magnitude is equal to the proct of the component of the force on the plane perpendicular to the axis and the vertical distance from the line of action of the component to the axis. The moment of a force to a point is the physical quantity of the rotation action of a force to an object around a certain point, which is equal to the vector proct of the position vector of the force acting point and the force vector
extended data:
Properties of moment:
1. The moment of force F to point O is not only determined by the force, but also related to the position of moment center. The moment varies with the position of the moment center
When the force is zero or the arm of force is zero, the moment is zero When the force moves along its action line, because the magnitude, direction and arm of the force do not change, the moment does not change The algebraic sum of the moments of two mutually balanced forces at the same point is equal to zerowhen an object is in static equilibrium, the static force is zero and the net moment to any point is zero. Moment is the derivative of angular momentum with time, just as force is the derivative of momentum with time. The angular momentum of a rigid body is the moment of inertia times the angular velocity
M = f * l
where m is the moment of force F on the rotation axis O. if the object has the effect of anti clockwise rotation, it is defined as positive moment, otherwise it is negative moment
unit: in the international system of units, the unit of moment is Newton * meter, abbreviated as Newton * meter, symbol: n * m
in physics, moment refers to the tendency of force to make an object rotate around the axis of rotation or fulcrum. The unit of moment is Newton meter. The Greek letter is tau
The concept ofmoment originated from Archimedes' research on lever. Rotational torque is also called torque or torque. Torque can change the rotational motion of an object. Pushing or pulling involves forces, while torsion involves moments. The moment is equal to the cross proct of the radial vector and the applied force
equilibrium conditions:
(1) the equilibrium of a body with a fixed axis of rotation means that the body is stationary or rotates uniformly around the axis of rotation
(2) the equilibrium condition of the object with fixed rotation axis is that the resultant moment is zero, that is, the sum of clockwise moment is equal to the sum of counter clockwise moment General equilibrium condition:the resultant force is zero and the resultant moment is zero at the same time, that is ∑ FX = 0, ∑ FY = 0, ∑ M = 0
torque:
(1) arm of force (L): the vertical distance from the rotation axis to the action line of force
(2) moment (m): M = L × F. The unit is n * M
(3) the moment describes the rotation effect of force on the object(4) torque is a vector, only clockwise and counterclockwise directions are considered in middle school. It is usually specified that the torque is positive counterclockwise and negative clockwise
extended data:
according to the international system of units, the unit of energy and work is Joule, which is defined as 1 Newton meter. But Joule is not a unit of moment. Because energy is a scalar of the distance of the proct of the force points; The moment is the pseudo vector of the distance cross proct force. Of course, the same dimension is not only a coincidence; It takes 2 * PI joules of energy to apply a 1 N-M moment to a full revolution
when an object is in static equilibrium, the static force is zero and the net moment to any point is zero. For two-dimensional space, the requirement of balance is:
x, Y direction resultant force is 0, and resultant moment is 0
Properties:1. The moment of force F to point O is not only determined by the force, but also related to the position of the moment center. The moment varies with the position of the moment center
When the force is zero or the arm of force is zero, the moment is zero When the force moves along its action line, because the magnitude, direction and arm of the force do not change, the moment does not change The algebraic sum of the moments of two mutually balanced forces at the same point is equal to zeroelectric field force between two charges: F = kq1q2 / R ^ 2, K is electrostatic constant
where: j-moment of inertia, β— Angular acceleration
when the cylindrical load rotates around its axis, the moment of inertia J = Mr ^ 2 / 2
where m is the mass of the cylinder, R is the radius of the cylinder
according to △ T seconds to △ T seconds ω The angular acceleration of the cylinder can be calculated according to the requirement of rotational / minute angular velocity β= △ ω/ In this way, according to the radius r, length L and material density ρ， Calculate the mass m and the moment of inertia J,
calculate the angular acceleration according to the required starting speed β， Then the torsion moment M can be calculated. Then select the motor according to M. At the same time, the driving power of the motor can be calculated according to the load speed and transmission ratio
at the same time, you also need to consider that the torque obtained at this time is the load torque and the actual torque of the motor after deceleration. The rated parameters of the motor all have this data, and then you can choose the suitable motor.
Calculation of "couple distance": vector method, M = R F, where R is the position vector from any point of one force to any point of another force. The combination of couple moments can be obtained from the sum of vectors in the couple system
Basic meaning: couple is two equal parallel forces whose resultant moment is equal to the proct of the distance between one of the parallel forces and the parallel force (called couple arm); Couple moment;, The moment of couple has nothing to do with the position of rotation axisworking characteristics:
1. The resultant force of the couple at any point on the action surface of the couple is zero; Therefore, it will not change the translational state of the object, only the rotational state of the object
Usually, the couple can only be balanced by the couple; But in fixed axis rotation, it can be balanced by circular force (i.e. torque) Keeping the moment and turning direction of the couple unchanged, changing the force in the couple and the length of the arm of the couple will not change its effect on the rigid body The space resultant force couple moment is the vector sum of each couple moment; The plane resultant couple moment is equal to the algebraic sum of the component couple moments The moment of couple is proced by the forces on two different action lines. The two forces are equal in magnitude and opposite in direction, and the moment of couple will proce pure rotation effect The moment of couple is a free vector, so it will proce the same effect wherever it acts on the object Property introction:the unit of couple moment is the same as that of moment; cattle × M (kg) × M / s) & quot; It means that the moment of couple is a vector, and the relationship between its direction and the direction of the two forces that make up the couple follows the right-hand spiral rule. For the object with fixed axis, under the action of couple, the object will rotate around the fixed axis; If there is no fixed axis, the object will rotate around the axis passing through the center of mass under the action of couple
{F: force between point charges (n), K: electrostatic constant, k = 9.0} × 10 ^ 9N · m ^ 2 / C ^ 2, Q1, Q2: electric quantity of two-point charges (c), R: distance between two-point charges (m), direction on their connecting line, force and reaction, same kind of charges repel each other, different kinds of charges attract each other}
3. Electric field strength: e = f / Q (definition formula, calculation formula, electric field strength is its own property, independent of electric field force and electric quantity) {e: electric field strength (n / C), electric field strength: e = f / Q (definition formula, calculation formula, electric field strength is independent of electric field force and electric quantity), 4. Electric field formed by vacuum point (source) charge e = KQ / r2
{R: distance from source charge to the position (m), Q: electric quantity of source charge}
5. Electric field strength of uniform electric field E = UAB / D {voltage (V) between two points of UAB: ab}, d: The distance between two points AB in the direction of field strength (m)}
6. Electric field force: F = Q * e
{F: electric field force (n), Q: electric quantity of charge under electric field force (c), e: electric field strength (n / C)}
7. Potential and potential difference: UAB = φ A- φ B，UAB＝WAB/q＝- Δ EAB / Q
8. Work done by electric field force: WAB = Q * UAB = EQ * d
{WAB: work done by electric field force from a to B (J), Q: charge (c), UAB: potential difference between a and B (V) (the work done by electric field force is independent of path), e: uniform electric field strength, D: distance between two points along the direction of field strength (m)}
9. Electric potential energy: EA = Q* φ A {EA: electric potential energy (J) of charged body at point a, Q: electric quantity (c), φ A: The potential (V) of point a}
10 Δ EAB = eb-ea {difference of electric potential energy of charged body from position a to position B}
11 Δ EAB = - WAB = - Q * UAB (the increment of electric potential energy is equal to the negative value of work done by electric field force) 12. Capacitance C = q / u (definition formula, calculation formula)
{C: capacitance (f), Q: electric quantity (c), u: voltage (potential difference between two plates) (V)}
13. Capacitance C of parallel plate capacitor = - ε S/4 π KD (s: the opposite area of the two plates, D: the vertical distance between the two plates, ε： The acceleration of charged particles in electric field (VO = 0): w = 0 Δ The deflection of charged particles entering uniform electric field with velocity VO along the direction of vertical electric field (without considering the effect of gravity) is similar to horizontal throwing vertical electric field direction: uniform linear motion L = VOT (E = u / D in parallel plates with equal amount of heterogeneous charges) parallel electric field direction: uniform acceleration linear motion d = at2 / 2 with initial velocity zero, A = f / M = QE / M
note: (1) when two identical charged metal spheres are in contact, the distribution of electric quantity is as follows: those with different charges are neutralized first and then equally divided, and those with the same charges are equally divided
(2) the electric field line starts from the positive charge and ends at the negative charge. The electric field line does not intersect, and the tangent direction is the direction of field strength. The electric field is strong in the dense part of the electric field line, and the electric potential is lower and lower along the electric field line, and the electric field line is perpendicular to the equipotential line
(3) the electric field line distribution of common electric fields should be memorized
(4) the electric field strength (vector) and electric potential (scalar) are determined by the electric field itself, and the electric field force and electric potential energy are also related to the amount of electric charge and the positive and negative charge of the charged body
(5) in electrostatic equilibrium, the conctor is an equipotential body, and the surface is an equipotential surface. The electric field line near the outer surface of the conctor is perpendicular to the surface of the conctor, and the combined electric field strength inside the conctor is zero. There is no net charge inside the conctor, and the net charge is only distributed on the outer surface of the conctor
(6) capacitance unit conversion: 1F = 10 ^ 6 μ F＝10^12pF
(7) EV is the unit of energy, 1eV = 1.60 × 10-19J
(8) other related contents: electrostatic shielding / oscilloscope, oscilloscope and its application / equipotential surface / tip discharge, etc
(9) electric field strength e = u / D = 4 π kQ/ ε S. And work w = u * q
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the "torque" of the motor, in N & # 8226; M (nm)
the formula is t = 9549 * P / n
P is the rated (output) power of the motor, and the unit is kW.
denominator is the rated speed, and the unit is R / min.
P and N can be found directly from the motor nameplate.
R: distance between two-point charges (m), direction on their connecting line, force and reaction, same kind of charges repel each other, different kinds of charges attract each other}
3. Electric field intensity: e = f / Q (definition formula, calculation formula) {e: electric field intensity (n / C), is vector (superposition principle of electric field), q: 4. Electric field formed by vacuum point (source) charge e = KQ / r2 {R: distance from source charge to the position (m), Q: electric quantity of source charge}
5. Electric field strength of uniform electric field E = UAB / D {voltage between UAB and ab (V), D: distance between AB and ab (m)}
6. Electric field force: F = QE {F: electric field force (n),}, q: Electric quantity (c) of electric charge under electric field force, e: electric field strength (n / C)}
7. Potential and potential difference: UAB = φ A- φ B,UAB＝WAB/q＝- Δ EAB / Q
8. Work done by electric field force: WAB = quab = eqd {WAB: work done by electric field force when charged body is from a to B (J), Q: charge (c),
UAB: potential difference between a and B in electric field (V) (work done by electric field force is independent of path), e: uniform electric field strength, D: distance between two points along the direction of field strength (m)}
9. Electric potential energy: EA = Q φ A {EA: electric potential energy (J) of charged body at point a, Q: electric quantity (c), φ A: The potential (V) of point a}
10. The change of potential energy Δ EAB = eb-ea {difference of electric potential energy of charged body from position a to position B}
11 Δ EAB = - WAB = - quab (the increment of electric potential energy is equal to the negative value of electric field force)
12. Capacitance C = q / u (definition formula, calculation formula) {C: capacitance (f), Q: electric quantity (c), u: voltage (potential difference between two plates) (V)}
13. Capacitance C of parallel plate capacitor = - ε S/4 π KD (s: the opposite area of the two plates, D: the vertical distance between the two plates, ω： Dielectric constant)
common capacitors
14. Acceleration of charged particles in electric field (VO = 0): w = 0 Δ EK or Qu = mvt2 / 2, Vt = (2qu / M) 1 / 2
15. Deflection of charged particles entering uniform electric field with velocity VO along the direction of vertical electric field (without considering the effect of gravity)
plane like vertical electric field direction: uniform linear motion L = VOT (E = u / D in parallel plates with equal heterogeneous charges)
throwing motion parallel electric field direction: uniformly accelerated linear motion d = at2 / 2 with initial velocity zero, A = f / M = QE / M
note:
(1) when two identical charged metal spheres are in contact, the distribution law of electric quantity is as follows: those with different charges are neutralized first and then equally divided, and those with the same charges are equally divided
(2) the electric field line starts from the positive charge and ends at the negative charge. The electric field line does not intersect, and the tangent direction is the direction of field strength. The electric field is strong in the dense part of the electric field line, and the electric potential is lower and lower along the electric field line, and the electric field line is perpendicular to the equipotential line
3) the electric field line distribution of common electric fields should be memorized
(4) the electric field strength (vector) and electric potential (scalar) are determined by the electric field itself, and the electric field force and electric potential energy are also related to the amount of electric charge and the positive and negative charge of the charged body
(5) in electrostatic equilibrium, the conctor is an equipotential body, and its surface is an equipotential surface. The electric field line near the outer surface of the conctor is perpendicular to the surface of the conctor, and the combined electric field strength inside the conctor is zero.
there is no net charge inside the conctor, and the net charge only distributes on the outer surface of the conctor< (6) capacitance unit conversion: 1F = 106 μ F＝1012PF
(7) EV is the unit of energy, 1eV = 1.60 × 10-19J