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Torque question (qualitative)

  1. Jun 3, 2016 #1
    1. The problem statement
    what role does torque play in body stability and ergonomics ?
     
  2. jcsd
  3. Jun 3, 2016 #2
    I'm not sure what level of explanation you want... Most simply, torque is a turning moment. The idea of torque is that if you apply a force at a greater distance, you get a bigger rotation - it would be easier to swing a cat by its tail than its middle (if you wished to swing cats), and it requires less effort to open a door from the edge, rather than at the pivot.

    If you want a mathematical definition:

    $$ \tau_{Total} = \sum_{i} \tau_{i} = \sum_{i} \vec{r_{i}} \times \vec{F_{i}} $$

    Where ##\tau_{Total}## is the total torque on the body, and is the sum of a number of torques, ##\tau_{i} = \vec{r_{i}} \times \vec{F_{i}}## where, ##\vec{r_{i}}## is the position vector, and ##\vec{F_{i}}## is the force.

    The angular momentum of a body is related to the torque applied:

    $$ \vec{L} = \vec{r} \times \vec{p} $$

    $$ \frac{d\vec{L}}{dt} = \frac{d\vec{r}}{dt} \times \vec{p} + \vec{r} \times \frac{d\vec{p}}{dt} $$

    So

    $$ \frac{d\vec{L}}{dt} = \vec{r} \times \vec{F} $$

    i.e -if we don't have any torque, then the angular momentum must be constant in time. The body cannot be spinning up or spinning down - in cannot be changing its motion in any rotational sense. So in this way, we see that a necessary (but not sufficient! - e.g we also have to balance forces) condition for equilibrium is that the total torques on a body must be zero...

    Does that help at all?
     
  4. Jun 3, 2016 #3

    CWatters

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    Penny... have a think about the joints in the human body. I think all (?) Involve rotation.
     
  5. Jun 3, 2016 #4
    The question is more geared towards when trying to improve stability or how do stability and torque correlate. I was thinking it had to do with Centre of mass or base of support. I have no idea what could be said for ergonomics
     
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