Calculate Torque on a Particle with Given Force and Position | Homework Solution

In summary, the torque on a particle about the origin can be found by taking the cross product of the force exerted on the particle and the distance from the pivot point. In this case, the torque is equal to 0i, 0j, -88k. It is important to remember the correct cyclic order when taking the cross product to get the correct signs.
  • #1
sp3sp2sp
100
4

Homework Statement


Force F⃗ =−11j^N is exerted on a particle at r⃗ = (8i^+5j^)m.
What is the torque on the particle about the origin? Express your answer using two significant figures. Enter coordinates numerically separated by commas.

Homework Equations

The Attempt at a Solution



F: 0i, -11j, 0k
r: 8i, 5j, 0k

F X r = (0-0)i - (0-0)k + (0 - -88)j
= 0, 0, 88

this is wrong because it should be -88, but I don't see why? It was my understanding that I should plug values into formula i - j + k. Thanks for any help.
 
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  • #2
sp3sp2sp said:

Homework Statement


Force F⃗ =−11j^N is exerted on a particle at r⃗ = (8i^+5j^)m.
What is the torque on the particle about the origin? Express your answer using two significant figures. Enter coordinates numerically separated by commas.

Homework Equations

The Attempt at a Solution



F: 0i, -11j, 0k
r: 8i, 5j, 0k

F X r = (0-0)i - (0-0)k + (0 - -88)j
= 0, 0, 88

this is wrong because it should be -88, but I don't see why? It was my understanding that I should plug values into formula i - j + k. Thanks for any help.

What's the definition of torque?
 
  • #3
sp3sp2sp said:

Homework Statement


Force F⃗ =−11j^N is exerted on a particle at r⃗ = (8i^+5j^)m.
What is the torque on the particle about the origin? Express your answer using two significant figures. Enter coordinates numerically separated by commas.

Homework Equations

The Attempt at a Solution



F: 0i, -11j, 0k
r: 8i, 5j, 0k

F X r = (0-0)i - (0-0)k + (0 - -88)j
= 0, 0, 88

this is wrong because it should be -88, but I don't see why? It was my understanding that I should plug values into formula i - j + k. Thanks for any help.

In future, please avoid using symbols like j^N; in typewriter math, this means ##j^N##, which is not what you intend. Just use j N, or perhaps enclose the "N" in parentheses, so write either F = - 11j N or F = -11j (N). Better still, use LaTeX to typeset your formulas and equations, so you could write ##F = - 11\, j## N or ##F = -11\, j## (N). You could even make them look like vectors by using a bold font, or an arrow on top, like this: ##\mathbf{F} = -11 \, \mathbf{j}## N or ##\vec{F} = -11 \vec{j}## N.

Anyway, back to your question. Is torque equal to ##\mathbf{r \times F}## or is it ##\mathbf{F \times r}##?
 
  • #4
Thanks for the replies . Torque is not communicative so torque = r X F
Its the cross product of the Force and the distance from pivot.
 
  • #5
OK I think i get it now. it should be in form rXF which when you apply the i-j+k gives 0i, 0j, -88k
thanks for help
 
  • #6
sp3sp2sp said:
when you apply the i-j+k
I am not familiar with such a formula. I assume it is some way to remember how to get the signs right, but if so I dislike it. It loses the symmetry.
It is really quite simple. The result is the next one around in cyclic order:
ixj->k
jxk->i
kxi->j
If you have to switch the inputs to get them in cyclic order, switch the sign too:
jxi->-k
kxj->-i
ixk->-j
 
  • #7
Yup that's exactly what it was .. its not a formula, just way I was remembering it because it was confusing me. thanks for the help
 

1. How do you calculate torque on a particle?

To calculate torque on a particle, you need to know the force acting on the particle and the position of the particle relative to the point of rotation. The formula for torque is T = r x F, where T is torque, r is the position vector, and F is the force vector.

2. What is the unit of torque?

The unit of torque is Newton-meters (Nm) in the SI system. In the imperial system, it is pound-feet (lb-ft) or foot-pounds (ft-lb).

3. How does the position of the particle affect the torque?

The position of the particle affects the torque as it determines the length of the lever arm. The longer the lever arm, the greater the torque will be. This means that the particle will experience a greater rotational force if it is further away from the point of rotation.

4. Can torque be negative?

Yes, torque can be negative. This occurs when the force and the position vectors are in opposite directions. Negative torque can also be referred to as clockwise torque, while positive torque is counterclockwise.

5. How is torque related to rotational motion?

Torque is directly related to rotational motion. It is the force that causes an object to rotate about an axis. The greater the torque, the greater the rotational acceleration of the object will be. This is described by the equation T = Iα, where I is the moment of inertia and α is the angular acceleration.

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