Help with derivation of torque equation T = p x E

In summary, torque (\vec{\tau}) is defined as the cross product of the force (\vec{F}) and the position vector (\vec{r}). Similarly, angular momentum (\vec{J}) is defined as the cross product of the position vector (\vec{r}) and the linear momentum (\vec{p}). This relationship allows us to calculate the torque on a particle using the rate of change of its angular momentum. Closing threads is not necessary.
  • #1
iScience
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[itex]\vec{\tau}[/itex]=[itex]\vec{F}[/itex]x[itex]\vec{r}[/itex]

[itex]\vec{F}[/itex]=[itex]\vec{E}[/itex]q

[itex]\vec{p}[/itex]=q[itex]\vec{d}[/itex]

[itex]\vec{\tau}[/itex]=([itex]\vec{E}[/itex]q)xr=[itex]\vec{E}[/itex]x[itex]\vec{p}[/itex]

so then how do we end up with [itex]\vec{\tau}[/itex]=[itex]\vec{p}[/itex]x[itex]\vec{E}[/itex]?
 
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  • #2
You need to tell us what you are trying to accomplish. What do your variables represent, what is your reasoning behind each step, etc.
 
  • #3
iScience said:
[itex]\vec{\tau}[/itex]=[itex]\vec{F}[/itex]x[itex]\vec{r}[/itex]

No, the definition is [itex]\vec \tau = \vec r \times \vec F[/itex]. At least, that's the definition in every textbook I've ever used.
 
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  • #4
The torque, [itex]\vec{\tau} [/itex], about a point, O, of a force, [itex]\vec{F} [/itex], acting at point P which is located at position [itex]\vec{r} [/itex] from O is DEFINED AS
[tex]\vec{\tau} = \vec{r} \times \vec{F}.[/tex]
As with all quantities in Physics, we would't define it as we do, unless what we've defined is useful. In this case, there is a simple relationship between the torque about O of a force acting on a particle, and the rate of change of the particle's angular momentum, [itex]\vec{J} [/itex] about O.

Namely
[tex]\vec{\tau} = \frac{d\vec{J}}{dt}.[/tex]
[itex]\vec{J} [/itex] is defined exactly analogously to [itex]\vec{\tau} [/itex], but substituting the particle’s linear momentum, [itex]\vec{p} [/itex], for the force, [itex]\vec{F} [/itex], on the particle, so...
[tex]\vec{J} = \vec{r} \times \vec{p}.[/tex]
 
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  • #5
jtbell said:
No, the definition is [itex]\vec \tau = \vec r \times \vec F[/itex]. At least, that's the definition in every textbook I've ever used.

thanks this answers everythingnow how do i close threads?
 
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  • #6
iScience said:
thanks this answers everything


now how do i close threads?

You don't.

Zz.
 

1. What is torque?

Torque is a measure of the rotational force applied to an object. It is calculated by multiplying the force applied to the object by the distance from the point of rotation to the point where the force is applied.

2. What does the letter "T" represent in the torque equation?

In the equation T = p x E, "T" represents torque.

3. What is the significance of the "p" and "E" in the torque equation?

"p" represents the magnitude of the force applied to the object, and "E" represents the distance from the point of rotation to the point where the force is applied. Together, they allow us to calculate the torque acting on an object.

4. How is the torque equation derived?

The torque equation is derived from the principle of moments, which states that in order for an object to be in rotational equilibrium, the sum of the clockwise moments must be equal to the sum of the counterclockwise moments. By applying this principle to the forces acting on an object, we can derive the torque equation.

5. What are the units of torque?

The units of torque are typically given in newton-meters (N·m) in the SI system of units. In the imperial system, they are given in foot-pounds (ft·lb).

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