What is Moment of force: Definition and 32 Discussions

In physics and mechanics, torque is the rotational equivalent of linear force. It is also referred to as the moment, moment of force, rotational force or turning effect, depending on the field of study. The concept originated with the studies by Archimedes of the usage of levers. Just as a linear force is a push or a pull, a torque can be thought of as a twist to an object around a specific axis. Another definition of torque is the product of the magnitude of the force and the perpendicular distance of the line of action of a force from the axis of rotation. The symbol for torque is typically


{\displaystyle {\boldsymbol {\tau }}}
or τ, the lowercase Greek letter tau. When being referred to as moment of force, it is commonly denoted by M.
In three dimensions, the torque is a pseudovector; for point particles, it is given by the cross product of the position vector (distance vector) and the force vector. The magnitude of torque of a rigid body depends on three quantities: the force applied, the lever arm vector connecting the point about which the torque is being measured to the point of force application, and the angle between the force and lever arm vectors. In symbols:






{\displaystyle {\boldsymbol {\tau }}=\mathbf {r} \times \mathbf {F} \,\!}






{\displaystyle \tau =\|\mathbf {r} \|\,\|\mathbf {F} \|\sin \theta \,\!}


{\displaystyle {\boldsymbol {\tau }}}
is the torque vector and


{\displaystyle \tau }
is the magnitude of the torque,


{\displaystyle \mathbf {r} }
is the position vector (a vector from the point about which the torque is being measured to the point where the force is applied),


{\displaystyle \mathbf {F} }
is the force vector,


{\displaystyle \times }
denotes the cross product, which produces a vector that is perpendicular to both r and F following the right-hand rule,


{\displaystyle \theta }
is the angle between the force vector and the lever arm vector.The SI unit for torque is the newton-metre (N⋅m). For more on the units of torque, see § Units.

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  1. D

    Book plots position & force on the same graph, still gets right answer

    In the picture you can see what I'm talking about. This is a simple problem to do if you can use moments, but alas my education system seems to have something against those. ##AB## is the uniform rod/ladder, G is its centre of mass, BE is the horizontal x axis, AD is the wall, BD is the smooth...
  2. S

    Think of a body which is at rest but not in equilibrium

    When a ball is thrown upward it becomes at rest at maximum height, at this it is not in equilibrium although it is at rest. It is not at equilibrium because force of gravity is acting on it? Still I cannot find good explanation from exam point of view.I also cannot find the figure/diagram.
  3. J

    A problem involving 'stress' and possible moment of force(?)

    Given, ##2A_P = A_Q## (cross-sections) ... (1) and, ##Y_P = 2Y_Q## ... (2) We have ##\frac {Y_P * x}{\Delta L} = \frac{Y_Q (L-x)}{\Delta L}## Using (2) in the above expression we get ##x = L/3## whereas the correct answer is ##x = 2L/3## I feel my initial idea is flawed, and that I am...
  4. A

    B Effort Force for a Wheelbarrow

    If you are using a wheelbarrow, the materials in it should be placed to as close as the fulcrum (the wheel) as possible. This is because the load torque of the materials will decrease, and the effort force required to support the wheel barrow will decrease as well, because Torque = Fr. Is this...
  5. G

    How can I find the length of this pole?

    Homework Statement A pole BC is supported by the cable AB as is shown in the figure. If the magnitude of the force applied on the point B is 70 lb, and the moment of this force about the x-axis is -763 lb ft, determine the pole lenght. I'LL ATTACH AN IMAGE SO YOU CAN SEE IT. Homework Equations...
  6. B

    The total moment when rolling

    Hey, everyone, I have a question regarding quadcopters, when the set of the arms is of configuration X, to roll we increase the velocity of the two motors on the left/right and decrease the other motors on right/left, the question is when doing so the total angular velocity is zero that means...
  7. M

    How to find the maximum moment of a force about an axis?

    Homework Statement Calculating the moment of force F about the axis isn't hard; how do I determine how to produce the maximum moment? Homework Equations Maxis = ûaxis ⋅ (r×F) F = 30N (This doesn't change at all during the problem) The Attempt at a Solution I would guess that since the...
  8. Soumalya

    Statics: Equilibrium in 3-Dimensions

    Homework Statement The portable reel is used to wind up and store an air hose. The tension in the hose is 100 N and a vertical 200-N force is applied to the handle in order to steady the reel frame. Determine the minimum force P which must be applied perpendicular to the handle DE and the...
  9. Soumalya

    Statics: Problem about Equilibrium in 3-dimensions

    Homework Statement The two uniform rectangular plates each weighing 800 kg are freely hinged about their common edge and suspended by the central cable and four symmetrical corner cables. Calculate the tension T in each of the corner cables and the tension T0 in the center cable. All...
  10. V

    Moment of force exerted by water on tube

    Homework Statement Homework Equations Bernoulli's equation : ##P + \frac{1}{2}ρv^2 + ρgh ## = constant The Attempt at a Solution The pressure at the interface is ##P_{int} = P_0 + ρgH## . Applying bernoulli's equation between point at the interface of two liquids and exit of the tube ...
  11. S

    Resultant Moment of Force Around Point O: 20 Nm Clockwise

    Homework Statement Calculate resultant moment of forces about pt O and state its direction.Homework Equations Put the picture. Check it outThe Attempt at a Solution What I did was : About A : 60Nm B: 40 Nm C : 120Nm. I'm not sure to add or subtract for resultant. What I did:: Add. A-B as they...
  12. M

    Moment of force from an axis - 3D problem

    Homework Statement An OAB pipe is embedded in O. A cable BC = 1000N and F = ( 0,-f , 0) act on B. Question: Determine the magnitude of the force F as the resultant moment about the axis OA is canceled. Picture in attachment: Homework EquationsThe Attempt at a Solution O=(0 0 0) A=(1.5 0 0)...
  13. L

    Moment of force and static equilibrium

    1) Problem: An individual holds a ball of mass 3 kg in his hand in static equilibrium. The biceps brachii attaches a distance of 2 cm from the centre of rotation of the elbow joint, and the muscle's line of action is directed at an angle of 115° counter clockwise from the forearm. The forearm...
  14. A

    Why torque is moment of force & angular momentum is moment of momentum

    Why the torque is called moment of force and angular momentum is called moment of linear momentum ? Please explain.
  15. B

    MHB Moment of Force F & P: Calculation & Solution

    I just don't know where did the numbers 5,4, and 3 came from. please explain. I'am asked to do this assuming clockwise moments as positive, compute the moment of force F = 200 kg and force P = 165 kg about points A, B, C, and D. the solution picture is here
  16. B

    Moment of force about a point

    Homework Statement The moment of force Fa about point O Homework Equations The Attempt at a Solution I know how to setup with breaking the force into x,y component but how to tell if its rotating cw or ccw about the point. I think y is ccw but i can't tell on x. I think i...
  17. Z

    Understanding Torque and Moment of Force: Explained with Energy Interpretation

    The way that I can understand how torque works is to say that the greater distance from the rotation axis that you apply your force, the greater power you are delivering to your object - since the farther you are away from the rotational centre the faster something is moving on your rotating...
  18. A

    Moment of force and Newtons 2nd law

    By the end of the day, I must admit that the rotational analog of Newtons 2nd law: Τ = I*α contradicts my intuition. Suppose that you take a part of a body in the radius r from the rotational axis and exert a force on that. It will then get a linear acceleration. We can then find the angular...
  19. F

    How to Solve Problems with Moment of Force in Physics

    Question in moment of force http://www.roo7oman.com/up/files/357062.jpg I find moment of Q correct but moment of p is not correct pleses I want your help
  20. A

    Comparing 'Moment of Force' and 'Moment of a Couple

    Are the 'moment of a force' and the 'moment of a couple' are technically same or different? Because, the latter is called by a special term 'torque'. Both terms are confusing, as the first is measured by the product of the force and its perpendicular distance from the fulcrum where as the...
  21. P

    What is the net force on a door with multiple forces acting on it?

    Homework Statement A regular house door has 3 forces acting on it.At the moment the door is open by 35 deg. Let's say two children are pushing on a door and mum is on the other side pushing back 1/ at 0.05m is 50N acting directly perpendicular to the door 2/ at 0.07m is 50N acting at right...
  22. L

    Moment of force ? some clarifications needed.

    Homework Statement Regarding the moment of force, this is the definition given in the book The tendency of rotation is called turning effect of a force or moment of the force about the given axis. The magnitude of the moment of force F about a point is defined as the product of the...
  23. R

    Moment of force, stabilising a board carried over shoulder

    Homework Statement A 3m board is carried and has a weight of 32N. 1.8m sticks out behind the carriers shoulder,1.2m in front and his hand is 0.4m from the shoulder.How much downward force needs to be applied at the hand to stabilise the board. Assume the weight is evenly distributed along the...
  24. G

    Moment of force and the meter rule

    Hi, I have a revision question, it's actually quite popular on the Internet but I would just like some help with it. A metre rule is supported on a knife-edge placed at the 40 cm graduation. It is found that the metre rule balances horizontally when a mass which has a weight of 0.45 N is...
  25. G

    Calculating Moment of Force on Bicycle Pedal

    Hi, I have a practice question. I have managed to calculate part of it and one last bit I haven't been able to. Hoping you can give me some ideas. I am given a bicycle pedal that is a some distance long and has been pushed downwards by a given force. Here I have been able to calculate the...
  26. T

    Calculating Moment of Force in Free Body Diagram

    [b]1. See following attatchment [b]2. Moment of force= (force)*(perpendicular distance) only for scalar problems. [b]3. Well i know that moments are a cause of roation among a certain point and when computing equilibrium we have to calculate the moment for every force on the free...
  27. M

    Calculating Moment of Force Produced at Point A

    Homework Statement In order to raise the lamp post from the position shown, force F is applied to the cable. If F = 200 lb, determine the moment produced by F about point A. I've attached the diagram. I apologize for the terrible quality. The length of the post from A to B is 20 ft...
  28. X

    Physics question on Moment of force

    Homework Statement A uniform metre ruler of weight of 1.2N suspended at its mid-point from a spring scale which is calibrated in Newton(N). An apple with weight of 0.75N, suspended from the metre rule at the 10cm mark, is balance by a weight of 1N, which is suspended from the 80cm mark...
  29. S

    Calculating Moment of Force in a Right Triangle - 3-4-5 Triangle Example

    Homework Statement I have a 3-4-5 right triangle with the 3 as the base and the 5 as the hypotenuse. The corner of the 3 and the 5 is point A The corner of the 3 and the 4 is point B At B, perpendicular to the base is a force of 100lb going down- into the corner. (Fv) At B...
  30. A

    Must d be Perpendicular Distance for Moment of Force?

    Moment of force= F*d*sin(alpha). Now, Must d be the perpedicular distance from the force to the axis , or any distance? Thanks in advance, Aladdin
  31. Saladsamurai

    Seriously? Moment of Force about a specified Axis

    [SOLVED] Seriously? Moment of Force about a specified Axis So I really thought I understood this. I have attached the problem and attempt at solution. It should be easy to follow. Problem Attempt at Solution This was my process: 1. Write each F and each r as cartesian vectors 2. Find...
  32. M

    Moment of force and tension

    hello, i have a problem i have having trouble solving, it reads as follows: a vertical pole is supported by two ropes, each 5m from the base of the pole. The rope to the right of the pole extends 3m up the pole, and the rope to the left of the pole extends 4.5m up the pole. The ropes and...