torque Definition and Topics - 480 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. 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)
  2. 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...
  3. 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)...
  4. 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...
  5. Istiakshovon

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  7. V

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  9. P

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  10. 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...
  11. 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...
  12. P

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    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...
  13. Matejxx1

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  14. T

    Derivation of torque on general current distribution

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  15. J

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  16. 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...
  17. 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...
  18. L

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  19. Jason234578

    Engineering Moment of a force about point O

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  20. enthusiast

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  21. B

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    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...
  22. 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...
  23. 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...
  24. 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.
  25. 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.
  26. 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) $$ \vec{\tau} = I \vec{A} \times \vec{B} $$
  27. 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...
  28. Shubol3D

    Calculate the output power for da Vinci's tank mechanism

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  29. 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!
  30. 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...
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