Torque Definition and 498 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




τ



{\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:





τ

=

r

×

F





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




τ
=


r





F


sin

θ




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





τ



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



τ


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





r



{\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),





F



{\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,




θ


{\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. H

    Sign hanging from massless beam attached to hinge supported by string

    Attempted creating equations for zeros of torque and components of forces in x and y as seen in picture. Got lost with having only variables and the d & 2L for the length of the beam. Not sure how to do the question with two points of contact between the beam and the sign. Is the center center...
  2. A

    I Required Strength of a Strap connecting 2 Rolls

    Hello, I am trying to figure the strength (in lbs) of a strap needed to attach 2 Rolls together without breaking. Each wheel has a weight of 1000lbs and a diameter of 30in. If there is required information missing, let me know.
  3. N

    Convert moment force at lever support

    I am trying to determine if a clamp holding a lever with a mass at one end can experience zero or reduced torque either by balancing the forces or converting the rotational torque into another form such as linear, I’ve looked at counterbalance with Steadicams etc. but I believe this just...
  4. T

    Cylinder Force Calculations

    I am trying to calculate the force required to lift/move the beam clockwise from the shown position. I have a force (F1) acting at the end of the beam, 5,000lbs pushing to the left, as shown. What is "Fcyl", or the force required by the cylinder to life the beam with the acting load, and rotate...
  5. Differentiate it

    A counterintuitive Laws of Motion problem

  6. tbn032

    B Unable to understand how these two forces are equal

    In the solution given in the above image, I am unable to understand and prove why N1=f and N2=W. I have tried balancing the torque on different point but still unable to prove. Explain how N1=f and N2=W can be proved. The justification for N1=f and N2=W which I have so far read is that it is...
  7. R

    Need help with Tension Control when rewinding industrial rolls of tape/films/liners

    So, this problem is going to require some explaining.. I'm a Production Engineer who's recently started working at an adhesive tape converter/distributor and I've been working on an industrial rewinding machine for films, tapes, foams etc. The tapes I rewind range from 0.2mm - 3mm thickness...
  8. rcgldr

    I Torque required to prevent precession

    A torque is applied to a spinning gyro, and a second torque is applied to prevent precession. How to quantify the second torque? Example, a gyro spinning about the z axis is connected to a frame that can only rotate about the x axis. A torque about the x-axis is applied to the frame. What is...
  9. ElectricVocaloid

    Dynamics problem (force and torque analysis) of a human finger

    I was having trouble with a physics problem (string tension dynamics) In this case I have a model that simulates the phalanges of a human finger. Each phalanx is a block of mass m1, m2 or m3 respectively. And to simplify it, consider the 3 equal masses. These phalanges are linked by joints that...
  10. M

    I Weight required to hang straight down with known torque

    How much Weight (W) is required to keep a weight hanging straight down when the torque is known on a rotating shaft? Please see attached image. Assume a lever weight of zero to keep it simple.
  11. James Brown

    B Will a round-headed rod topple if it slides down a frictionless slope?

    Well, the problem is that, someone told me that a ball won't roll when sliding down a frictionless slope because the resultant force mgsinx is parallel to the slope which means that the ball will slide down the slope. Now, replace the ball with a round headed rod, does this means that the rod...
  12. A

    Magnetic field with loop

    I am confused about this, do the black arrows represent the direction of magnetic force? The torque ##\tau = -IABsin\theta##, where I = current A is area of loop and B is magnetic field strength and I am a little confused how ##\theta## here is 45 degrees when the angle between the normal for...
  13. L

    Disk with rod attached rotating about the center of the disk

    1) Since the rod is uniform, with mass m and length l, it has a linear mass density of ##\lambda=\frac{m}{l}##, so ##I_{rod_O}=\int_{x=r}^{x=r+l}x^2 \lambda dx=\frac{\lambda}{3}[(r+l)^3-r^3]=\frac{\lambda r^3}{3}[(1+\frac{l}{r})^3-1]=\frac{1}{3}mr^2[3+\frac{3l}{r}+\frac{l^2}{r^2}].##...
  14. L

    A sphere rolling without slipping down a hemisphere

    a) From impulse-momentum theorem I have: ##J=mv## so ##v=\frac{J}{m}## and since the ball doesn't slip ##v=\Omega b## so ##\Omega=\frac{J}{mb}## and ##\dot{\theta}=\frac{v}{a+b}=\frac{\Omega b}{a+b}##. b) I considered the angular impulse: ##-J(a+b)=I_0 \Omega_0 \Rightarrow...
  15. M

    Engineering Torque calculation of a motor with permanent magnets

    $$Vstator_{peak} = 120√2 *√2 = 240 V$$ $$Istator_{peak} = i_{q} (current on q axis)= 20*√2 = 28.2842 A $$ $$ω{15} = Ω_{15} * p = 2π * 15 = 94.2477 rad/s$$ $$ω{15} = Ω_{15} * ψ_{pm}$$ Hence $$ψ_{pm} = e0/ω15 = 168.3V/94.2477 rad/s => ψ_{pm} = 1.79 Wb$$ $$M = 3/2 * p * ψ_{pm} * iq $$ Hence $$ M...
  16. curiousPep

    I What are the criteria to decide which equations will give the motion of a gyro-compass?

    Hello, I know it might sound silly but sometimes I get confused. Let's say I have a gyro-compass and I get 3 equations of torque for the 3 axes. I am expected to find the equation of motion and two of them are equated with 0. These are the Euler's dynamics equation with moving reference frame...
  17. jonas_biermann

    B Calculating the torque needed to rotate a drum

    Imagine this: You have a drum with a radius of 12cm, around that drum is a toothed belt which is connected to a motor. The drum weighs 10kg The motor should be placed under the drum How would I calculate the amount of torque needed to rotate the drum I don't have any idea how to calculate this...
  18. T

    A Cylinder Rolling in a V-Groove

    I am confused because according to my solution the disk is already rotating at constant angular velocity. I have written the translational equilibrium on the horizontal and vertical component: ##N_1## and ##f_2## will have a positive horizontal contribution, while ##N_2## and ##f_1## will have a...
  19. Father_Ing

    Torque formula derivation for a particle moving in circular

    Consider that the particle is moving in circular with tangential velocity v, and (0,0)is its origin. I wonder why dr/dt is equal to tangential velocity instead of radial velocity (since dr/dt means how much change in radial distance in a really short duration of time)
  20. RalphZ

    Automotive Does vehicle weight have an effect on torque capacity of the gearbox?

    Hi, This has long been in my head, I've seen it work out in reality, but I have no idea about the forces involved in this. As I don't have an engineering degree or mathematical knowledge in automotive engineering, I've come here for help. Sorry if I've used some terms where they do not fit, as...
  21. L

    Tangential velocity of rotating rod

    1) ##LT\sin(\frac{\pi}{2}-\theta)-\frac{L}{2}mg\sin\theta=0\Rightarrow T=\frac{mg}{2}\tan\theta##. ##N_{x}-T=0, N_{y}-mg=0\Rightarrow N=\sqrt{N_x ^2+N_y ^2}=mg\sqrt{(\frac{\tan\theta}{2})^2 +1}## 2) ##E_{k_{fin}}=mg\frac{L}{2}[1+\cos\theta]## 3)...
  22. G

    Torque calculations: Rotating vertical shaft

    I apologize in advance for any errors in my concepts or assumptions. Feel free to correct me wherever I am wrong. Thanks in advance for the help. There is a vertical shaft which will be operated at around 600 rpm (N) which can be achieved in 2 seconds (or even 4 just an assumption). The shaft...
  23. Istiak

    How long does it take for the disk to stop rotating?

    Question : Solution attempt : for
  24. brotherbobby

    Force of water against a dam gate

    Question : I start by putting the image of the problem from the book. The water surface is given to run along the (top) edge of the bridge. Attempt : The crux of this problem lies in the fact that the pressure of water against the gate will vary along its depth ##h## as ##\rho gh##. This makes...
  25. V

    Ideal Vs Real Mass Pulley system

    Below is an ideal mass pulley system that we encounter in many problems under Newton's Second Law of Motion questions. Its supposed to be massless and frictionless i.e. string slips over the pulley and pulley does not rotate. In a real system, the pulley is assumed to be massless, whereas in...
  26. hang

    Seesaw with spring and plate

  27. P

    Rotating ring in a B-field

    Summary:: Please see the attached photo. I have obtained the correct answer, and my solution agrees with the official solution. However, I have some questions about why the solution is correct. (One may have to draw out some diagrams for this problem, it was quite hard to visualise for me.)...
  28. C

    Automotive Need help calculating load torque and acceleration torque of a vehicle

    Hi everyone, I'm working on designing a vehicle that uses electric motors, but I'm having a little trouble finding the load and acceleration torques in order to select the right motors to use. Variables: m = total mass of vehicle a = acceleration μ_r = rolling friction coefficient r = wheel...
  29. K

    Finding the torque required for telescopic cable mechanism

    Summary:: I am designing a linear telescopic system that gets elevated with a step motor, but in order to find the compatible motor, I need to work out the torque that is required for the elevation. I have uploaded my CAD model to this thread with how cables are connected. Could someone please...
  30. P

    I Does the Normal contact force act through the centre of mass?

    Consider the following situation: You have 1 rectangular block lying on a table, and an identical block is placed above the block on the table. Now, this new block is constantly pushed to the right, right before it topples off. Consider the torque about an axis passing through the rightmost...
  31. Matejxx1

    Describe the motion of yoyos suspended from the ceiling

    I have trouble solving this problem any help would be appreciated. Problem statement ##J=\frac{mr^2}{2}## a) Determine the motion of yoyos for ##n=1,2,3## The case for ##n=1## is simple, however, I am having trouble with ##n=2## and ##n=3##. for ##n=2## I started by drawing all the forces...
  32. U

    Derivation of torque on general current distribution

    How do I simplify the expression...
  33. J

    Mass rotating but with string that's decreasing in length over time: work done

    For the displacement, how do I figure out the angle theta between the points? And how does the speed at which the string retracts affect the centripetal force?
  34. G

    How to calculate the magnitudes of three forces around a hexagon

    Can anyone please help me with the following? Three forces which act along the sides AB, BC and CD of a regular hexagon ABCDEF of side 2a, have a resultant which acts along DF. When a couple of 4Pa in the sense CBA is added in the plane of the hexagon, the resultant acts along CA. Find the...
  35. M

    Help with flywheel / clutch calculations

    Hey everyone, I have a problem with sizing a clutch for my machine. My problem is, I don't know how to calculate the needed value (Nm) for the clutch to withstand the torque affected by the flywheel. I have a flywheel that weighs 90kg and is 600mm in diameter. It is rotating at 500rpm...
  36. L

    DIY Simple analog engine dynamometer -- How to do it?

    Hi, I have to measure the HP of a small engine at the crankshaft. The only usable things are. A dinamometer A brake disk An rpm meter The brake caliper is floating so when we apply de load it pull the dinamometer. The rpm meter show the revolution during the load apply. It can works? How I...
  37. Jason234578

    Engineering Moment of a force about point O

    G'day. I have a problem with my statics work, i understand its probably quite simple but I am having trouble in my understanding. Essentially problems make more sense to me by using the component method, although in saying that i understand this problem would be quite a lot more simple were i to...
  38. enthusiast

    Mechanics: A bowling ball is thrown and rolls with slipping

    Summary:: A bowling ball is thrown on a bowling lane with the coefficient of friction ##\mu## with an initial velocity of ##v_0## and no rotation. After hitting the ground, it starts rolling with slipping. After how much time after hitting the lane will the ball stop slipping? What will be its...
  39. B

    Confusion About Rotational Motion

    I watched a video that showed how to calculate the center of gravity of a horizontal bar suspended from two wires, one attached to each end. Each wire was then attached to a vertical wall. The angle each wire made with the wall it was attached to was given. They treated it as an a example of...
  40. P

    Automotive Vehicle Parking Brake Test on a Slope [How Convert to a Flat Ground test?]

    Vehicle Mass : 3 tonnes Manufacturer's instruction is to test vehicle's parking brake effectiveness is to engage parking brake on 30.96 degrees slope. If it holds, it is effective. I do not have 30.96 degrees slope & I want to replicate the same test on flat ground. I was thinking of...
  41. Y

    Moment of inertia where mass and torque are at a different positions

    The formula for moment of inertia is: I=mr^2 A common derivation for this is: 1. F=ma 2. τ=rma 3. τ=rmrα = r^2 mα This is a rotational version of Newton’s second law, where torque replaces force, moment of inertia replaces mass, and angular acceleration replaces tangential acceleration...
  42. cupcake_rainbow

    Question on torque balancing

    So I tried using force balancing. I have attached files of my solution in my notebook Torque balancing about O which gives me equation 1 And I used property of triangle, for equation 2 But i can't seem to get the right answer Also, I was wondering if it could be done by concept of virtual work.
  43. R

    Determining moment (or torque) around a certain point on a wrench

    Here's a diagram of the problem. There are 3 possible solutions: 163 in-lb clockwise, 163 in-lb counterclockwise, 82.7 clockwise or none of them. After attempting the problem the closest I got to was 82.7 but that was wrong so I'm still stuck.
  44. Leo Liu

    Torque on a circular current loop

    Can anyone please tell me why the torque on a circular current loop can be calculated by the equation below? In other words, what is the intuition for the formula? Thank you. (I modified my question to a particular case) $$ \vec{\tau} = I \vec{A} \times \vec{B} $$
  45. Adesh

    What force will be felt by ##B## when a rod is rotated?

    We have a rod ##AB## of mass ##m##, a force (perpendicular to AB) is applied at ##A##. I want to know how much force will ##B## going to feel? When ##F_1## is applied at ##A## rod will rotate about its COM (which lies at the Center) and hence the point ##B## will also move (a little downwards...
  46. Shubol3D

    Calculate the output power for da Vinci's tank mechanism

    Hello everyone. I'm working on 3D animation about da Vinci tank and why it doesn't work. Please help me find out how to compute: 1: how many men need to move this machine 2: what power on wheel can produce different number of man, like 1, 2, 4, 8.. vehicle mass = 8t men strength = 60kg lever...
  47. L

    Integral for the calculation of torque

    Hello, I found an integral to calculate the torque from the applied torsional shear stress, and I didn't find an explanation of how this integral is deviated. Where does it come from? Could someone explain? T = ∫τ⋅r⋅dA = ∫τ⋅2πr⋅dr, where T is the torque and τ the shear stress. Thanks a lot!
  48. O

    Analytical mathematical modeling of the torque caused by the laundry

    Hello my dear physicists, I'm trying to model the varied generated (needed)Torque to rotate a washing machine Drum during a Washing Process so i assumed that the Model has as Input the target vilocity and as an Output the new needed torque to rotate the Drum(to be as a input for the motor...
  49. S

    Vertical Load Torque

    If I'm to choose a motor to suit a vertical load (torque)-see the attached picture for more illustration-. What is the criteria should i follow? After i have done the math for the weight of the object to be rotated, the torque to rotate the load is to be horizontal, and i only have the weight...
  50. O

    The torque (and stalling torque) of a servo motor

    I'm using a servo to lift a pen. The pen and a bit of mechanism weights 35g. The servo I use to bring the pen up and down claims to have a torsional moment of 1.5kg/cm. Sometimes they call it torque in the specs. But surely that does not mean they are claiming that if I hung a 1.5kg weight a...
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