unknown user

11-07-2007, 09:31 AM

Dear subscribers,

I agree with Young Hoo Kwon on everything he wrote except this:

"I beileve we call dH/dt (rate of change in angular momentum) torque,

but not moment of force..."

Young Hoo is a brilliant biomechanist, and his web site is a source of

precious information for many of us, but in this case he is wrong. There's a

crystal clear difference between the torque applied on a body and the

derivative of its angular momentum. The first is the cause, the other is the

possible effect.

According to the equation of motion by Newton and Euler, the torque by a

force on a body is equivalent to the derivative of its angular momentum

(i.e. they happen to have the same value) only if it is equal to the total

torque acting on the body (i.e. when it is the only torque acting on the

body, or when the other torques add up to zero). Also, the equivalence holds

only if the point with respect to which the torque and angular moment are

computed is the center of mass of the body or a point fixed in an inertial

reference frame.

An analogous difference exists between force and linear momentum derivative.

All I wrote above regarding torque is also valid for the moment of a force.

As I wrote in my previous message, some authors (especially engineers, as

far as I know) give to the word "torque" a stricter meaning. Nobody gives it

a broader meaning.

It is perhaps of some interest to remind in this context that the word

"moment", when not followed by "of a force" or "of a couple", has a much

broader meaning than the word torque. As well as the word "momentum" (which

has a very different meaning, even in current english), the word "moment"

comes from the Latin "movimentum" (movement), and is also used to mean

"instant of time". This too low specificity (and too high ambiguity) of the

word is the reason why some authors prefer using the word "torque".

With kind regards,

Paolo de Leva

I agree with Young Hoo Kwon on everything he wrote except this:

"I beileve we call dH/dt (rate of change in angular momentum) torque,

but not moment of force..."

Young Hoo is a brilliant biomechanist, and his web site is a source of

precious information for many of us, but in this case he is wrong. There's a

crystal clear difference between the torque applied on a body and the

derivative of its angular momentum. The first is the cause, the other is the

possible effect.

According to the equation of motion by Newton and Euler, the torque by a

force on a body is equivalent to the derivative of its angular momentum

(i.e. they happen to have the same value) only if it is equal to the total

torque acting on the body (i.e. when it is the only torque acting on the

body, or when the other torques add up to zero). Also, the equivalence holds

only if the point with respect to which the torque and angular moment are

computed is the center of mass of the body or a point fixed in an inertial

reference frame.

An analogous difference exists between force and linear momentum derivative.

All I wrote above regarding torque is also valid for the moment of a force.

As I wrote in my previous message, some authors (especially engineers, as

far as I know) give to the word "torque" a stricter meaning. Nobody gives it

a broader meaning.

It is perhaps of some interest to remind in this context that the word

"moment", when not followed by "of a force" or "of a couple", has a much

broader meaning than the word torque. As well as the word "momentum" (which

has a very different meaning, even in current english), the word "moment"

comes from the Latin "movimentum" (movement), and is also used to mean

"instant of time". This too low specificity (and too high ambiguity) of the

word is the reason why some authors prefer using the word "torque".

With kind regards,

Paolo de Leva