# Torque Force Mass Question

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Hi,

Torque = Distance * Force

Torque = Distance * Mass * Linear Acceleration

These equations are for particles.

If I'm using a wrench, is the Mass the total of the particles in my hand?

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Posted (edited)

Nope, because your muscles and skeleton will deflect the force your arm applies to the end of the wrench into the ground.

You use Torque = Force * Length of the lever * sin(angle at which the force is applied to the lever).

The force it self must be known in this equation, e.g. a weight force or some such.

Edited by Green_Baron
Nonsense deletd ;-)

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what u say doesn't make sense.

The mass in these equations stays the same. It's not the mass of the person that matters.

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Posted (edited)

I deleted one part that really didn't make sense 😉

If i understand you correctly you want to calculate a torque but do not know the force that's applied to the lever, is that right ?

You need to know the force your hand excerts. The force is the outcome of the work of the muscles and the skeleton of the person standing on the ground. It is not the number of particles in the person's hand. In the above case, the force must be known to solve the equation.

Edited by Green_Baron

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Torque = Distance * Mass * Linear Acceleration  (for a particle)

If I use a 3D wrench, What constitutes the Mass?

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Posted (edited)
10 minutes ago, Cacks said:

Torque = Distance * Mass * Linear Acceleration  (for a particle)

If I use a 3D wrench, What constitutes the Mass?

Almost correct. For the lever, you need the angle at which the force is applied as well, that is the sin term, or you assume that the force is always applied at 90° to the wrench all the way round.

For a child on a seesaw for example you know the mass (lets say 30kg) and the acceleration (9.81m/s² at sea level) and the angle is ~90° for the whole way it travels, for a hand pulling a wrench this is not the case. You must know the force and the angle at which it pulls to solve the equation (edit: for torque, or know the torque to solve for mass).

Mass is not applicable here, one must know or estimate the force at which the human pulls the wrench.

Edited by Green_Baron

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yeah 90 degree angle always to simplify

I disagree, the mass is applicable since it's in the equation

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Vector from screw position to hand centered position (where you hold the wrench) x force applied (vector)

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Posted (edited)

If i understand it right, the force is unknown. In this case, the formula for a force being mass * acceleration can't be applied like it could with a weight dangling from a lever (Harold Lloyd comes to my mind :-)) or a child on a seesaw.

Instead, the concept of work being done by the muscles should be used. That'll be Force = work/(displacement*angle) or so. But calculating the work isn't trivial and would differ from person to person. Perhaps it would just suffice to use a statistic figure from ergonomics, like 30kg or so ...

But i don't pretend to be right, just a suggestion.

Edited by Green_Baron

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Posted (edited)

Hi,
If that can help with the question when considering rotational motions the equivalent of the mass in linear dynamics is the moment of inertia (around the rotation axis here, it's more complicated with more degrees of freedom)

Torque [N*m] = moment of inertia [kg*m²] * angular acceleration [rad/s²]

There are some examples about how to compute moments of inertia here.

Edited by D.C.Elington

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