What is the Initial Torque of a Rod with an Acting Force?

In summary, the conversation discusses a rod initially positioned on the y-axis with a length of ℓ and a force acting at the upper end. The question asks for the initial torque about the lower end of the rod, with 5 possible answers listed. A hint is given to use the definition of torque in terms of a cross product.
  • #1
shiby4444
4
0

Homework Statement



A rod is initially along the y-axis and has
length ℓ. A force F =ˆı F1 +ˆj F2 + ˆk F3
acts at the upper end of the rod.
What is the initial torque ~τ about the lower
end of the rod?
1. Zero
2. ˆıF3 ℓ
3. −(ˆı F3 +ˆj F2 + ˆk F1) ℓ
4. (ˆıF3 − ˆk F1) ℓ
5. (ˆıF1 +ˆj F2 +ˆk F3) ℓ


Homework Equations





The Attempt at a Solution

 
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  • #2


Hint: What's the definition of torque in terms of a cross product?
 
  • #3


Doc Al said:
Hint: What's the definition of torque in terms of a cross product?

I am not sure. Please help
 
  • #4


[tex]\vec{\tau} = \vec{r} \times \vec{F}[/tex]
 
  • #5


What answer would that be with respect to my choices?
 
  • #6


shiby4444 said:
What answer would that be with respect to my choices?
That's for you to figure out! All I did was give a definition of torque. Hint: Find an expression for [itex]\vec{r}[/itex] (its magnitude is ℓ) and perform the cross product.
 

What is the initial torque?

The initial torque is the amount of rotational force applied to an object at the beginning of a rotational motion. It is the starting point for measuring the change in rotational motion.

How is the initial torque calculated?

The initial torque can be calculated by multiplying the force applied to an object by the distance from the axis of rotation at which the force is applied. This can be expressed as the formula T = F x r, where T is the torque, F is the force, and r is the distance from the axis of rotation.

What is the unit of measurement for initial torque?

The unit of measurement for initial torque is Newton-meters (Nm) in the International System of Units (SI). In some cases, it may also be expressed in foot-pounds (ft-lb) in the imperial system of measurement.

Why is initial torque important?

Initial torque is important because it determines the initial rate at which an object will start to rotate. It is also a key factor in determining the overall rotational speed and acceleration of an object.

How does initial torque differ from static torque?

Initial torque and static torque are essentially the same, except for the fact that initial torque is measured at the start of rotational motion while static torque is measured when an object is already in motion. Both involve the application of a force at a distance from the axis of rotation.

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