What is Moment arm: Definition and 13 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. B

    Analyse the cutting force of this bolt cutter

    The question is to determine the force in the small opening, delivered from the 250 N on both sides of the plier. i tried multiple things but can't get the answer right. Anyone that could help me? This is my work so far:
  2. bardia sepehrnia

    Statics problem (moment and equilibrium)

    1. Having really hard time understanding the concept of moment and equilibrium in statics. In the following picture the man is carrying a 6kg uniform rigid board. I'm asked to calculate the amount of force the man feels on his shoulder. (at point A) Now I know I'm supposed to start by making...
  3. F

    Solving a Homework Problem with One Pivot

    Homework Statement https://cdn.discordapp.com/attachments/373928512811302912/528638926148337704/question.PNG part a )50N I cannot answer part b. Homework Equations M=FD The Attempt at a Solution Ok so if both pivots were in contact with the beam I would just equate them with the oppposite...
  4. Beth N

    Equilibrium of Rigid Bodies. Rafter. What is moment arm?

    Homework Statement Two uniform 150 N rafters rest on frictionless floor, held together by a rope. A 500 N load is held at their apex. Find tension in the tie rope. Homework Equations ##torque= rFsin \theta =Force*Moment Arm ## The Attempt at a Solution The angle ##\theta## in the picture...
  5. P

    Moment Arm: Determine Torque Vector & Qty

    Homework Statement I'm trying to determine the torque vector and quantity of said vector per the sketch attached. Homework Equations T=fd[/B] The Attempt at a Solution T = 100 lbs x 2 f2f T= 200 ftlbs But my real question is where is that Force being applied at is it the attachment point...
  6. M

    I Can a bicycle be tipped over by only applying rear brake?

    Let's say I'm riding a bike at constant speed. Also assume that the person riding is rigid, no moving of the persons body, constant center of gravity. Assuming that there is sufficient friction between the tires and road. If I apply the front brakes, I will likely tip over. If I apply the...
  7. A

    B Effort Force for a Wheelbarrow

    If you are using a wheelbarrow, the materials in it should be placed to as close as the fulcrum (the wheel) as possible. This is because the load torque of the materials will decrease, and the effort force required to support the wheel barrow will decrease as well, because Torque = Fr. Is this...
  8. Diptangshu

    Are Moment Arm & Common Perpendicular Different?

    Not only the Problem I have attached in Picture, but there are few more where I get different answer while solving by taking Moment Component and by Common Perpendicular. [NB : The problem Stated in 'Engineering Mechanics' by Ferdinand L. Singer. Process 3 is what I did, Process 1 is what is...
  9. RoboNerd

    Angular Acceleration and Moment Arm

    Homework Statement [A rocket has landed on Planet X, which has half the radius of Earth. An astronaut onboard the rocket weighs twice as much on Planet X as on Earth. If the escape velocity for the rocket taking off from Earth is v , then its escape velocity on Planet X is a) 2 v b) (√2)v c) v...
  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. S

    Problem with the weigth of the moment arm

    Hi A rod comprises a counterweight (a) a handle and a hook which hangs mass (m), the rods mass is 400g counterweight mass (a) = 1600g and the rod is 0.8m long. Equilibrium exists when the handle is at position X = 12.0cm How I did 1: calculated the length of the handle to (m) which was...
  12. joema

    Angular acceleration given force, moment arm and inertia?

    Homework Statement Find angular acceleration in deg/sec^2 given the following factors: - Total mass: 4889 kg - Moment of inertia: 4620 kg*m^2 - Moment arm length from center of mass: 1.5 meters - Force on moment arm tangent to mass: 1779 Newtons Homework Equations torque = force...
  13. Z

    What is the length of the moment arm.

    So here's the problem: Bodybuilder “Hulk” Heise is doing leg curls on a Cybex machine. “Hulk” gets stuck (see figure) with 90° angle at the knee joint. The force exerted by the machines (FA) on his leg is 500 N, directed at an angle of 55° (angle α) relative to the tibia, and the distance...