What is Lever arm: Definition and 22 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


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






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


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


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


{\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),


{\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,


{\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. Fury22

    B Lever balancing physics (video game design)

    Hi everyone! I am not a physicist or a physics student. Just a simple video game programmer. I have recently gotten into a discussion with my fellow programmer about a specific hypothetical problem regarding levers. The problem might seem very simple at first, but cause me a bit of headache...
  2. nateTheaweseome

    Understanding and Troubleshooting Handlebar Load Calculations

    Hey all, I'm either overthinking it or too tired but this problem should be an easy one to figure out but I'm stumped embarrassingly. Say in the photo above is a lever arm. I'm trying to backtrack to calculate the force a user must input (yellow) against a force (red). It can pivot around...
  3. MattGeo

    Torque and Moment of Inertia of a Lever Arm

    I never really considered this back when I was taking physics in college but imagine for the sake of thought experiment that you have an extremely and impractically long wrench and it is fixed to the bolt you wish to tighten. Now the longer the lever arm the greater the torque so if you double...
  4. R

    Would a longer lever require less force to hand pump water? (PHOTO)

    I think that it would take less force to pump water based on the lever principle. But I'm not so sure! Here's a drawn photo.
  5. A

    Compound lever arm - compressor design

    So what comes to mind is utilising the full height and further node points in a triangulated system... however being only just now introduced to the concept of a compound lever I am unsure of how to get this system to work. Any thoughts much appreciated.
  6. T

    Force applied to lever arm to twist foot pound torque

    If i need 1000 foot pound torque of 1000 foot pounds twisted very easily How long should the lever arm be and and how much force at the end of lever arm is required ? Tony Singh
  7. S

    Rotational Motion Question, lever arm with two masses

    Homework Statement [/B] A uniform rigid rod with mass Mr = 2.7 kg, length L = 3.1 m rotates in the vertical xy plane about a frictionless pivot through its center. Two point-like particles m1 and m2, with masses m1 = 6.7 kg and m2 = 1.6 kg, are attached at the ends of the rod. What is the...
  8. P

    Calculating the dimensions of a lever and a column

    Hi, I have a system with a lever arm that's attached to a vertical support at its pivot point. The lever is pushed up by hand and is supported by a stay lid like in the image. I need to calculate the area and thickness of the arm and the column but the only numbers I have is the load attached...
  9. B

    Mechanical advantage: lever arm

    Homework Statement In order to lift the 30 kg mass, a Force F is applied to the massless meter stick shown below. How much weight must the fulcrum bear if the mass is to be lifted? Homework Equations R/E = l/L The Attempt at a Solution So I began with the formula above and this is my set up...
  10. x2017

    Trouble Determining Moment Arm (aka Lever Arm)

    Homework Statement Homework Equations ΣM=Στ The Attempt at a Solution I know how to get the net torque about point P, but I am having difficulty determining where the moment arms for each force should be. I did 9 simpler questions before this no problem, but this diagram is a bit more...
  11. C

    Confusion about how to identify lever arm

    Homework Statement A rotational axis is directed perpendicular to the plane of a square and is located as shown in the drawing. Two forces, F1 and F2, are applied to diagonally opposite corners, and act along the sides of the square, first as shown in part a and then as shown in part b of the...
  12. C

    Solving a Lever System: Lever Arm and Load Lengths

    Forgive me if this is in the wrong category. I have a product I am working out - I am a programmer and electronic engineer by trade, which didn't include a lot of work with physics principles. I have a lever system which seems simple - but the trick is, my load is acting as a lever too...
  13. F

    Calculating Torque and Lever Arm

    Here is the problem http://imgur.com/6KRKJQu Torque = force x lever arm We are told that the force is all the same so the only thing that would determine the torque is the size of the lever arm. The ones that I'm not sure about are B and C. The rest I think I have done correctly. Just to make...
  14. N

    Greatest Lever Arm: Calculating Force at Elbow Joint

    Homework Statement The diagram is attached. It is asking which position has the greatest lever arm.Homework Equations The Attempt at a Solution So, I know that the elbow is the fulcrum but what I'm struggling with is how to draw the force arrow. Where is the force coming from and where is it...
  15. D

    Force in The X direction using Lever Arm

    Homework Statement What is the Force Needed in the X direction? I have a 500 lb Car and attached to the Wheel axle is a 12 inch long lever arm going straight down. The pivot point is at the axle and a cylinder is pushing the arm at the end of it. What force do I need to push this 500...
  16. T

    Calculating torque when the lever arm has mass

    Homework Statement A board is set on top of a scaffolding, with dimensions as shown in the diagram. The board weighs 15 kg. A man weighing 70 kg stands on the board as shown. How far out can he stand before the board falls? Homework Equations Torque: \tau = rFsin(\theta) Force due...
  17. K

    Why does a Lever arm magnify force?

    Hey, I'm looking for an explanation of the why we observe T = F * d In the sense of two people applying a force to a lever arm and the person closer to the pivot point requiring more force to keep the torque in equilibrium. I can only find explanations in the sense of work and energy...
  18. D

    What is the lenght of the lever arm? (when torque and force are given)

    Homework Statement If a torque of 55N.m is required and the largest force that can be exerted by you is 135N, what is the length of the lever arm that must be used? Homework Equations Lever Arm=(r)(sin) Torque=(Force)(r)(sin) The Attempt at a Solution To be honest, I'm stumped
  19. E

    Torque Of Lever Arm in 1st/2nd Class Levers

    Part 1 - Question About Torque Of Lever Arm in a 1st Class Lever Homework Statement A little while back I posted a question about incorporating the torque of a uniform mass and dimension lever arm into the principle of a 1st class lever. Here is the thread for reference...
  20. D

    Calculating Torque & Lever Arm for a Lunch Tray

    A lunch tray is being held in one hand. The mass of the tray itself is 0.201 kg, and its center of gravity is located at its geometrical center. On the tray is a 1.33 kg plate of food and a 0.285 kg cup of coffee. Assume lever arm of the thumb is 0.0620 m, lever arm of the finger is 0.113 m...
  21. D

    Optimizing Lever Arm Length and Material for Maximum Distance in a Mousetrap Car

    am doing mine for distance should i have a long lever arm or a short lever arm, and how long should it be? and should i use a like a rubber string or just a normal one and how long should that be? thanks if you can reply by today