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:
{\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.
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...
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.
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...
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...
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...
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...
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...
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...
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.
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...
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...
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}].##...
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...
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...
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...
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...
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)
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...
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...
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...
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...
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.)...
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...
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...
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...
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##
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for ##n=2## I started by drawing all the forces...
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?
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...
Hey everyone,
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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
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The rpm meter show the revolution during the load apply. It can works?
How I...
G'day.
I have a problem with my statics work, i understand its probably quite simple but I am having trouble in my understanding.
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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...
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...
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...
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.
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.
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)
$$ \vec{\tau} = I \vec{A} \times \vec{B} $$
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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...
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!
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...
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?
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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...