# What is Torque and rotation: Definition and 52 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. ### Calculating Torque on this Square

So I started by just figuring out what forces are going to have torque. I know the one heading straight down from the pivot won’t have any and the one going at an angle from the pivot won’t be included in the net torque since it’s at the pivot. The rest of the forces have torque and they are...
2. ### Tipping Point of Stationary Barbell

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3. ### I What is torque exactly?

From what I understand about torque, it is basically the power of the force to cause a change in an object's rotational motion. It is easier to cause this change when the force is applied further from the point of rotation than closer, which is why it is difficult to open a door by pressing a...
4. ### I Moment of Inertia about an axis and Torque about a point

Angular Momentum and Torque are defined about a point. But Moment of Inertia of a body is defined about an axis. There are equations which connect Angular momentum and Torque with Moment of Inertia. How will this be consistent? When I say that the torque of a force acting on a body about a point...
5. ### B Rolling Motion Test: Take the Challenge and Justify Your Answers

I am posting this to generate a parallel discussion to this ongoing thread. It seems that some participants in that thread have doubts and confusion about rolling motion that might be better addressed separately from the homework problem in question. It is a simple test of one's understanding...
6. ### Time period of 2 disks connected by a spring

My attempt at solving case B I've attached my attempt at case B above. What problem I'm facing is that after writing equation of angular SHM, I'm getting angular acceleration proportional to cube of angular displacement, which doesn't reduce to SHM. So how to find time period for this...
7. ### Freely hinged rods on a table - Linear velocities of CM after the impulse

We know that impulse is $$\vec J = \vec F \Delta t = \Delta \vec p$$ Let ##l, m## be the length of single rod and its mass respectively. Analyzing torques and forces on each rod separately we have: Rod ##AC##: $$F\Delta t +N_x\Delta t = mV_{ac,x} \space\space\text{ eq. }(1)$$ F\Delta t\cdot...
8. ### Help solving garden gate statics problem

I am installing a garden gate at the back of my house. The length (L) of the gate is 1.7m and the mass is 62.6kg, there are 2 hinges positioned 1.3m apart. The gate has an inherent sag, such that, the bottom corner on the unhinged side is 5cm lower than the corner on the hinged side. What...
9. ### Displacement & Angle Theta: Figuring Out Centripetal Force

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?
10. ### Torque and Force question -- Multipe forces acting on an object

I have attempted and got 2 different solution 1: 2:
11. ### Find the Right Motor for a 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...
12. ### 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...
13. ### Show that the flywheel inside the train counteracts lean in a curve

Summary: Consider a train carriage rolling along a curve that forms a left turn on the track. The carriage speed is directed along the y-axis (into the plane of the paper) in the figure. The trolley will have a tendency to curl in the curve in the specified direction. A flywheel is inserted...
14. ### Rigid object in equilibrium

Here's the task: My attempt at a solution (I choose C as an axis): However, the textbook solution says D should be 58.8. What am I doing wrong?
15. ### Rotating Disk and Hanging Mass Calcululations

I used the above equations to solve for tension, torque, inertia, and angular acceleration. Are the formulas I used correct for the given system? How can I calculate Inertia from the trendline equation, I'm drawing a blank.
16. ### Find the acceleration and the work done by a force pulling a spool?

I already solved the first part, but according the my book, the answer isn't quite correct. This is what I did. Finally, I ended up with ##a=\frac{F(r-R\cos\alpha)}{Rm(\gamma+1)}##. But according to my book, the answer is ##a=\frac{F(\cos\alpha-\frac{r}{R})}{m(1+\gamma)}##, what am I doing...
17. ### CFD analysis of a turbine, interpreting torque values

Hello, I am using CFD to analyse a Kaplan turbine and am unsure on how to interpret the torque values as they come as x, y and z components. My understanding is that the z component in this case will determine the rotation direction depending on whether it is positive or negative however I am...
18. ### Rotational Movement of a Disc

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19. ### A question about magnetism that causes a wheel-loop to rotate

This question is from 1977 AP Physics C so I suppose it would be clear enough, but I am confused about question c. Question a is easy (it rotates counterclockwise), question b too (Στ=6*rxF=6*r x (I*i x B)=0.06). Question C is where I am stuck. The diagram provided with the question looks like...
20. ### How do I use τ = Iα here?

Homework Statement A uniform rod is released on a friction-less horizontal surface from rest. Initially, the rod makes an angle θ = 60° with the horizontal. What is the acceleration of the center of mass of the rod, just after release? Homework Equations Torque = Moment of Inertia × Angular...
21. ### How does mechanical torque affect generator volts and amps?

Hello! today I have a question regarding the most efficient way to generate electricity by moving a magnet across a coil. The theoretical magnet would be moving in a circular motion fixed to the outer circumference of a driver wheel like in many simple generators, how does the physical torque...
22. ### Calculate the magnitude and direction of the torque

Homework Statement [/B] a) (a) Assuming the HCl molecule consists of point-like ions (H+ and Cl) separated by 1.0 * 10^-10m, find the dipole moment of the molecule. b) Calculate the magnitude and direction of the torque exerted on this dipole if the molecule is subjected to an external electric...
23. ### Slowly Rotating Device For a Camera Pan Timelapse

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24. ### Torque of a rotating wheel on a static wheel

Homework Statement A uniform cylindrical wheel of mass ##m_{1}## and radius ##R_{1}## rotates with angular velocity ##\omega_{1}##. It lies a certain distance (along the same axis) from a static wheel of radius ##R_{2}## and mass ##m_{2}##. The wheels are then pushed against each other with a...
25. ### Rod w/ Pivot and Attached Mass Pendulum

Homework Statement A solid rod of length L and mass M has a pivot through its center and is originally horizontal. Another mass 2M is then attached firmly to one end of the rod, and released. What is the maximum speed of the mass 2M attained thereafter? (Cornell 2009) Homework Equations Not...
26. ### Torque & Rotation: 2 Axes, Tilting Possible?

I have some questions about torque and its role in gymnastics, or with anything that may rotate, possibly. First, is it possible for someone or something to use torque to rotate in two different axes of rotation at once? In a separate situation, is it possible to tilt using torque to tilt the...
27. ### Find Value of tan φ of Reaction Force | Isaac Physics

1. Find the value of tan φ to 2 sf where φ is angle made by line of action of reaction force at hinge above horizontal. https://isaacphysics.org/questions/trapdoor_num Part B Angle of reaction force Homework Equations Mass of uniform trapdoor: m=4.0kgm=4.0kg The trapdoor is held open...
28. ### Max ω of circular hoop rotating around a peg and oscillation

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29. ### Calculating the torque required to rotate a ski on snow

Hello friends, I'm currently working on an engineering competition project known as the Great Northern Concrete Toboggan Race, and I'm stuck on some preliminary calculations. I'm trying to calculate the amount of torque that will be required to rotate the front skis in order to turn the...
30. ### Torque and force question

Question that’s been boggling my mind. If you have a 1 ft torque wrench and your tightening your wheels on you Car and apply a force of 70 pounds 1 ft from the nut I’m applying 70 pounds of downward force on the nut but applying a much larger torque to the nut. Now if I apply a 70 lb force 3”...
31. ### Force required to tip a block

1. The problem statement, all variables, and given/known data If I apply a force perpendicular to the side of a 2D block at 1/2 its height with a fixed bottom corner opposite the applied force how much force will be required to tip the block?: Block Mass = M Block Width = W Block Height = H...
32. P

### Rotation vs Translation for elbow joint

If I were to cut the string and let the board move, I know I would get rotation. But, since the center of mass of the beam is moving as well (in a circle) could I also say that the board is translating once the string is cut?
33. ### Question about torque and center of mass

Supposing that we have a hollow sphere of mass m and radius R. Furthermore, suppose that we attach the sphere to a rod of length L and mass M. Now, suppose we rest the rod-sphere contraption on a pyramid a distance (X+R) from the center of mass of the sphere and a distance [(L/2)-X)] from the...
34. ### Sphere sliding up a step - Inelastic Collision

Homework Statement A sphere of radius R is rolling without slipping with a velocity v and collides inelastically with a step of height h < R. ¿What is the minimum velocity for which the sphere will be over the step? Homework Equations Total kinetic energy (maybe)...
35. ### Can someone confirm my answers on a few torsion problems?

Homework Statement Homework Equations The Attempt at a Solution I feel I did something wrong, but not sure where is my problem. I don't feel conformable on number 26 and 27 and 29, can someone please tell me which answer is incorrect and any tip on solving it would be greatly appreciated!
36. ### Rotational motion down an incline (ring/hoop)

Homework Statement A 24kg metal ring with 24cm diameter rolls without slipping down a 30 degree incline from a height of 3.4 m. 1) According to the law of conservation of energy what should be the linear speed of the ring at the bottom of the ramp 2) if the ring has a moment of inertia of...
37. ### Free Body Diagram lab report -- General Question

< Mentor Note -- thread moved to HH from the technical forums to use a scpecific schoolwork problem to illustrate the general concept of torque in a FBD > I'm writing up a lab report for Physics class and I have to draw FBDs for torque being applied to a ruler resting on a pivot point. I've...
38. ### Torque and rotation around a fixed point

This isn't a real homework problem (i.e. I made this problem up myself for my own purposes), but I figured this is the correct forum to post. 1. Homework Statement In the following figure we have two rods connected to each other, and the bottom rod is connected to the blue structure (G)...
39. ### Moment of inertia of a rigid body

Homework Statement Determine the moment of inertia of a rigid body on the picture: The radius of the inner cylinder is R and the outer is 2R. Homework Equations 3. The Attempt at a Solution [/B] I thought of subtracting the big cylinder inertia from the small and adding the hanging body and...
40. ### Torque and forces parallel vs perpendicular to the axis of rotation....

why force parallel to the axis of rotation do not make any torque.
41. ### Torque, beam, angular acceleration problem

Homework Statement [/B] A thin, uniform, 3.8kg bar, 80cm long has two 2.5 kg balls glued on at either end. It is supported horizontally by a thin, horizontal, frictionless axle passing through its centers and perpendicular to the bar. Suddenly the right hand ball becomes detached and falls off...
42. ### Rotating Friction Discs For Project Design

The situation is part of a mechanism I have been working on. It is used for a bicycle to automatically store and release energy with a spring. It is somewhat similar to a car clutch. Homework Statement Two friction discs are rotating with different angular velocities and different torques. The...
43. ### Max Force on a single rototiller blade

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44. ### Calculate linear acceleration of a pivoted stick

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45. ### Potential Energy for dipole in Electric Field

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46. ### How can I find the inertia of a rod with a pivot point?

I have a question on finding the inertia of a rod with a pivot point somewhere along it's length. So the inertia of a rod is IStick cm = 1/12 *m*L2 Does L2 = (2L/3)2 = 4L2/9 -> 1/12 *m*[4L2/9] or is it something like m*L2/12 + m* (2L/3)2? If it's the second one then may I ask why it's that...
47. ### Calculate motor/gear ratio on single axis

Firstly, let me explain that I am mostly inept at mathematics. Piecing together the required information is becoming a real challenge because of that. I am motorizing a dobsonian telescope. I have read many accounts of success and the steps involved. The places where detail is commonly left out...
48. ### Pulling power ratio for a cable drum at different capacities

Prior to my life as a database administrator I was a hi lead logger in coastal British Columbia, which involves harvesting logs with machines capable of putting huge strain on cable and hydraulic systems. What got me to thinking this was a friend just let me know someone we know was recently...
49. ### Find Moment of Inertia

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50. ### Motor Torque Calculation for Amusement Ride

Hi I'm looking for some info and advice. I've looked across the Internet and forums looking at different formulas for working out the torque requirements for a motor but can't find anything that helps me. I have designed a small amusement ride. Please see pic below. The outer ring...