# 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. ### 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. ### 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. ### 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. ### 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...

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

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10. ### 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. ### 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. ### 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. ### 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. ### 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...

45. ### 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. ### 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. ### 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. ### 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...