What is Torques: Definition and 106 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. E

    What is the angle of static equilibrium for a ladder on ice?

    tried equating torques around the pivots of the ladder and equating them to zero but I'm not getting anywhere with that.
  2. T

    Frequency & Wavelength of a Vibrating Wire

    Good morning, I'm working through the problem from the homework statement above and answered it correctly, but I can't help but feel that something important is missing. I was able to correctly identify the sum of torques by using the following diagram, where the CCW rotational direction...
  3. Lotto

    What is the smallest value of angular displacement of the raft?

    What is meant by "the smallest value of angular displacement of the raft from its original position during one cycle"? I understand that I am supposed to solve this problem using torques of the crane and and of the boxes, but I am totally confused by that "smallest angular displacement". If it...
  4. paulimerci

    Torques exerted on a vertical disk by multiple forces

    This was how the solution was arrived in the text, Net torque = F block x d block x sin ϴ0 + F rod x d rod x sin ϴ0 - T R sin 90 0 = 2mg x 2R x sin ϴ0 + m x R x sinϴ0 - T R T = 5 mg sinϴ0 I'm wondering do we have to resolve the forces for rod and block in to...
  5. paulimerci

    Torques on a vertical wheel due to 3 masses spaced along the wheel rim

    Applying rotational equilibrium at the center pivot we get: +mg(R) + Mg(Rcos60°)–2Mg(R) = 0.Using cos60° = ½ we arrive at the answer 3M/2 I don't understand why cosine is used instead of sine in the above equation. I see the y component mg is acting perpendicular to the x component and so from...
  6. L

    A slanted cylinder full of liquid about to fall

    The cylinder will cease to be in equilibrium when the sum of the torques on the cylinder calculated with respect to the rightmost point of contact of the cylinder with the plane will be unbalanced. Now, the liquid is homogeneous and the cylinder has negiglible mass so the forces (normal force of...
  7. K

    I Why is there no torque along this axis?

    Kleppner and Kolenkow say "Consider a gyrocompass consisting of a balanced spinning disk a light frame supported by a horizontal axle. The assembly is turntable rotating at steady angular velocity Ω. There cannot be any torque along the horizontal AB axis because the axle is pivoted". I'm not...
  8. V

    How can I add Moments / Torques in different planes?

    I have a problem as shown in the figure So assume there is a cylinder rotating inside a stationally wall. There is a viscous fluid in between the gap of cylinder wall and outer stationary wall, similar to bearing. The fluid has some velocity in axial direction also the outer wall of cylinder...
  9. Q

    Proper free-body diagram for a shaft experiencing multiple torques

    I wish to draw a proper free-body diagram for this shaft. However, my FBD does not agree with the solutions manual. If someone could point out where I erred, that would be great. This is what I drew: From my FBD, it is clear that the maximum torque is present in section DE of the shaft. We...
  10. A

    Why Doesn't the Ball Rotate When Hit by a Pivoting Rod?

    Okay, I asked this post(below) the other day on how ang. momentum was conserved by the ball. The answer was the ball receives an equal torque back from the door...
  11. S

    Can I get help solving this bottle opener problem using torques?

    Hi guys I'm studying at home over lock down would anybody be able to point me in the direction of some online learning material or what concept I should look up to solve this problem and find formulas . I'm stuck and can't find anything relevant online while searching. Thanks guys any help is...
  12. kepherax

    Using Forces and Torques to solve a pulley problem

    I am able to solve this easily using energy conservation, but I'm curious how one would go about solving this using forces and torques?
  13. J

    Sum of torques, equilibrium problem

    For part a, A force must be applied so that the entire mass can be 'held up'. Therefore the necessary force must be equal to the gravitation force on all the objects: m(rod) * 9.8 + m(LB) * 9.8 + m(RB) * 9.8 = 137 N For part b, (This is where I'm confused) let's set the point at which the...
  14. H

    Equation for sum of torques on a ladder and minimum angle

    Homework Statement [/B] Homework Equations Drawing a diagram for the forces is the easy part. I am not sure I am doing the equation of the sum of the torques well. The Attempt at a Solution This is my attempt for the forces[/B] And this for the torques:
  15. S

    What is the torque on the bolt due to the worker and the weight of the beam?

    Homework Statement A 3.60-m-long, 500 kg steel uniform beam extends horizontally from the point where it has been bolted to the framework of a new building under construction. A 70kg construction worker stands at the far end of the beam What is the magnitude of the torque about the bolt due to...
  16. B

    Can I add all torques in a shaft and use it as the Tmax?

    I have a problem on determining the diameter of a shaft. And I am required to find its maximum twisting moment/maximum torque (Tmax). Is it possible to add all the torques in different points of a shaft to be able to use it as the maximum torque (Tmax)?
  17. NoahCygnus

    A question about angular momentum and torques....

    There is something I don't quite understand about the law of conservation of angular momentum. Let's say a person is rotating about an axis passing through his/her centre of mass, with an angular speed speed ω1, and has a rotational inertia I1 about about the centre of mass. No torque is acting...
  18. mastermechanic

    Automotive How can torques be summed algebrally?

    Everytime I hear some informations in videos like "...car has 700Nm torque from ICE and additional torque of 400Nm from electric motor so total torque 1100 Nm" I can't understand how torques can be summed algebrally. My teacher said if the design is clever enough it can be done and said...
  19. E

    Sum of Torques in Equilibrium

    Homework Statement Two ladders, 4.00 m and 3.00 m long, are hinged at point A and tied together by a horizontal rope 0.90 m above the floor (Fig. P11.89). The ladders weigh 480 N and 360 N, respectively, and the center of gravity of each is at its center. Assume that the floor is freshly waxed...
  20. doktorwho

    Help understanding torques and moments

    Homework Statement Find the period of small oscillation of this system. Homework Equations 3. The Attempt at a Solution [/B] I understand the concept of moment of inertia but can't comprehend the first equaion here. The other two i get and they are moments of inertia of other two bodies...
  21. H

    Equilibrium Problem - Balancing Torques

    Homework Statement [/B] A door 1.00 m wide and 2.00 m high weighs 330 N and is supported by two hinges, one 0.50 m from the top and the other 0.50 m from the bottom. Each hinge supports half the total weight of the door. Assuming that the door’s center of gravity is at its center, find the...
  22. J

    Zero equilibrium 0 x a force?

    Okay - a classic trap . multiplication times zero . I have a 3 foot bar weighing 10 lbs . its attached along its mid point to an axle . how much torque / force - do I need along its axle ( motorized ) to get it to spin 30 rpm or 60 rpm ? its in equilibrium , but of course it needs FORCE...
  23. M

    Torques in a Pump: Understand Opposite Signs

    Hi In a pump (which operates in normal condition: steady state), pump torque is positive and fluid torque is of equal magnitude and of opposite direction so that the sum of both is zero. ''P. 66 of 'Water Hammer: An Analysis of Plumbing Systems, Intrusion, and Pump Operation' by: Dr. Loganathan...
  24. RoboNerd

    Question on torques. quick one.

    Homework Statement Homework Equations ok, I thought that the torque from the mass 'm' would be equal to torque from mass 'M' The Attempt at a Solution I wrote down: m * g * (d/4) = M * g * d (m/4) = M m = 4M Thus, the ratio is 4M : 1 m, which gives answer 1. However, the solutions say...
  25. RoboNerd

    Question about static equilibrium

    1. Homework Statement problem is above Homework Equations sum of torques = I * angular acceleration = 0 for rotational equilibrium The Attempt at a Solution OK, here's what I tried to do. I wrote sigma Fy = Fleft pier up + F secondleftpierup - Fg,beam = 0 I assumed that the two piers have...
  26. W

    Solving acceleration of a car with torques

    Hi! I cannot get rid of a mass and having some confusion about this whole problem. 1. Homework Statement A car's wheelbase is 300 cm and its center of gravity horizontal distance from rear axle is 120 cm and its distance from the ground is 75 cm. Wheels and ground's coefficient of friction...
  27. S

    Static Equilibrium: holding a sign

    Homework Statement You are holding a sign as shown below. The sign (including the horizontal bar it hangs from) has a mass of 2.20 kg and is 40.5 cm wide. The sign is hanging from a 1.03 m tall, 4.46 kg vertical post. The sign is symmetric with a uniform mass distribution as implied by the...
  28. tarchuletta

    How to use Moments of Inertia to find Max Acceleration (sportbike pre-wheelie)

    So in this problem there's a lot of leeway as far as parameters go. The numbers I give for weights, dimensions, etc, may not be super realistic, but that's not too important to me because I can plug in realistic numbers later. I more of need help understanding the concept of moments of inertia...
  29. R

    Are these torques correct for a simple balancing/fulcrum exp

    Homework Statement For my physics lab, they had us do a simple static equilibrium experiment where we rested a ruler on a fulcrum (at its center of mass) and then attached varying amounts of weight on either end at different distances from the fulcrum. This screenshot is the data we recorded...
  30. C

    Answer Torque Question: Find Allowable Shear Stress

    Hey, How would you realize if a shaft can resist a torque or not given an allowable shear stress and allowable angle of twist. Can I use the factor of safety? Thanks.
  31. Priyadarshini

    What is the torque needed to lift a weight with a lever?

    Homework Statement Homework Equations Torque=one of the forces x the perpendicular distance moment=force x perpendicular distance The Attempt at a Solution moment of pulling the weight up around the disc: 1.2/2 = 0.6 m 0.6-0.2 = 0.4 m moment= 0.4 x 900 = 360 Nm To lift it, the torque of the...
  32. erickbq

    [Statics - Torques] Determining Coefficient of Static Friction

    Homework Statement The top of a ladder of L and mass m is connected to a wall by a horizontal cable. The ladder makes an angle Θ=60 with the horizontal. A woman of mass 2m finds that as she climbs the ladder, the ladder begins to slip when she is one-third of the way up the ladder. Find the...
  33. erickbq

    [Statics - Torques] Determining the tension of a string

    Homework Statement A 10.0kg sphere is attached to the incline by a horizontal string. Determine the tension in the string. Homework Equations (F⃗ net)x=ΣFx=0 (F⃗ net)y=ΣFy=0 Στ=0 τ = (radial disance)(F) The Attempt at a Solution 1. I began by determining all the relevant forces associated...
  34. S

    Virtual Work & Quadcopter Torques: Exploring Rotational Dynamics

    Here is what we know from virtual work: $$ \delta W=\sum_{i=1}^N{\vec F_i\cdot\delta\vec r_{i}} $$ Where ##N## is the number of bodies in the system. I am considering a quadcopter, modeled as a rigid body so it is just one body and we have: $$ \delta W=\vec F\cdot\delta\vec r $$ My question...
  35. E

    Rotational motion-why are torques not in opposite directions

    Homework Statement A cylinder of mass m is suspended through 2 strings wrapped around it at its ends, connected to the ceiling. Both strings have equal tension, and the cylinder rolls without slipping. r is the distance between the CM of the cylinder and each end. I is the moment of inertia of...
  36. O

    Velocity and Torques Problem

    Homework Statement A uniform cylindrical spool of mass M and radius R unwinds an essentially massless rope under the weight of a mass m. If R = 12 cm, M = 400 gm and m = 50 gm, find the speed of m after it has descended 50 cm starting from rest. Solve the problem twice: once using Newton's...
  37. Jackson Lee

    Torques between revolving magnet bars

    Hey, guys, I find a interesting phenomenon. When an external magnetic field is applied on a current loop, the net torque will try to align the loop's dipole moment with the magnetic field. And considering that electrical loops could be regarded as electromagnet, we change the current loop into a...
  38. D

    Calculating Torques on a Door with Hinges

    Homework Statement Consider a do or, hanging on two hinges (s ee figure). The do or is L tall and d wide, and the hinges are placed at heights L/4 (point A) and 3 L/4 (point B) from the floor. The door is uniform, and so its centre of mass is in the middle of the door (point C) b) What is the...
  39. gcombina

    Ratio of Lengths b/a for Torques Equilibrium

    Homework Statement A 3.0-kg ball and a 1.0-kg ball are placed at opposite ends of a massless beam so that the system is in equilibrium as shown. Note: The drawing is not drawn to scale. What is the ratio of the lengths, b/a? (a) 2.0 (c) 3.0 (e) 5.0 (b) 2.5 (d) 4.0 Homework...
  40. O

    Torque & Normals: Why Do We Ignore Normals?

    Hi, I'm struggling to understand why we never consider normals when doing torque questions? One on the top of my head is a hand pushing a bar, 'x' metres away' from the pivot joint. From the worked examples, there is only one torque (the hand), but how come we never consider the normal...
  41. T

    Internal and external torques.

    How do I tell if a torque on a system is internal or external before conserving angular momentum? I know that if a force has its reactionary force in the system, then it is an internal force and we can conserve the linear momentum of the system. But I don't know how to recognize a reactionary...
  42. N

    Balancing a plank on springs (Torques)

    Hello, I would like some help with the following question. I highly appreciate your help ! I got an answer that doesn't make sense so I know there must be a concept that I don't get. There is a complicated piece of machinery sitting on a plank of metal which is 2 m long. The metal and...
  43. S

    Summing Torques about a square

    Homework Statement A square metal plate 0.180 m on each side is pivoted about an axis through point O at its center and perpendicular to the plate (Figure 1) . Calculate the net torque about this axis due to the three forces shown in the figure if the magnitudes of the forces are F1 = 25.0N ...
  44. B

    How Do Equal and Opposite Torques Work with Different Moment Arms?

    Angular momentum is conserved, which means that the change in angular momentum of object A must be exactly canceled by the change in angular momentum of the object exerting a torque on object A. So, the objects, A and B, exert equal and opposite torques on each other. But, the contact forces...
  45. H

    Rotational Dynamics: Net Torques

    Homework Statement Answer: C Note: Sorry admins for the picture, needed to include the diagram though. Homework Equations ∑\tau = I\alpha ∑F = ma a = \alphar The Attempt at a Solution The torques must be balanced (is this reasoning already wrong?), thus, F*R1 = F_T*R2 F_T =...
  46. S

    Classical Mechanics-Moments of Inertia and Torques

    Homework Statement a)Two people are holding the ends of a plank of length l and mass M. Show that, if one suddenly let's go, the initial acceleration of the free end (aD) is 3g/2. (7 marks). Moment of inertia, I, of the plank about its centre of mass is given by I=1/12(Ml2) b)Show...
  47. B

    How does torque help us understand the motion of objects?

    It's not a homework problem as I am way too old already but it's something that had made me given problem getting to sleep. I'm probably missing smthg. let's say you have a horizontal uniform rod lying on ice such as there is no friction and the normal force equal the weight of the rod. Let's...
  48. S

    Torques in equilibrium w/ angle

    on a meter stick the pivot point is placed at 1/4 its length; predict the force needed to balance the meter stick by pulling upward on the end of it with a string making an angle of 30 degrees w/ respect to the vertical. Me trying to solve it: sigma T=0 T1+T2=0 T1 = 0 <--this is the pivot...
  49. S

    Solving a Physics Problem with Friction: Directions of Forces and Torques

    Homework Statement Hi Im trying to solve this question, and I have the solution of it in front of me, but I really can't understand why its true. The question is this: A bowl with radius R is given, it can't move. In it there's a ball with radius r << R, and a mass m. Find... (lots of...