Finding torque (vector cross product)

In summary, the conversation discusses finding the torque about an axis through the origin and through a specific point perpendicular to the xy plane. The direction of the torque is determined using the right hand rule and the cross product method. For the second question, the position vector for the new axis is given and the position vector for the force point of application can be used to calculate the new position vector. The resulting torque is positive in direction.
  • #1
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A particle position is described by position vector r = 3i + 2j and the force vector i - 2j acts on the object.

1) Find the torque about an axis through the origin and perpendicular to the xy plane. Draw the two vectors to check your torque direction.

I used the right hand rule and found out that the torque will have a negative direction. Then I used cross product term by term.

My torque is -8 k NM.

2) Find the torque about an axis through the point x = 5m, y = 5m perpendicular to the xy plane. Draw the two vectors to check your torque direction. The force should produce a roation about (5,5) consistent with your answer.

How do I do this? The answer is 7 z Nm. Do I find the torque the same way as for part 1, and then somehow take the distance between them into consideration? How come the direction is now positive?
 
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  • #2
Ok the first question was pretty straightforward, they gave you the position vector from the origin to your force point of application. Now for the 2nd question you have another position. They give you the position vector for the other axis, and you have the position vector for your force point of application. Therefore, you can calculate the new position vector from the new axis position to your force of application. Remember is from the new axis position to your force point of application.
 
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  • #3




For part 1, the torque can be calculated using the formula T = r x F, where r is the position vector and F is the force vector. In this case, r = 3i + 2j and F = i - 2j. Plugging these values into the formula, we get:

T = (3i + 2j) x (i - 2j)
= 3i x i - 3i x 2j + 2j x i - 2j x (-2j)
= 0 - 6k + 2k - 0
= -8k

Since the torque is in the negative k direction, this means that the object will rotate clockwise around the origin.

For part 2, we can use the same formula but we need to take into consideration the distance between the axis and the point of rotation. The torque will be calculated using the formula T = (r - r0) x F, where r is the position vector, r0 is the position vector of the axis (in this case, (5i + 5j)) and F is the force vector. So, we have:

T = (3i + 2j - 5i - 5j) x (i - 2j)
= -2i - 3j x i + 4i - 5j x (-2j)
= 0 - 3k + 4k - 0
= 7k

Since the torque is in the positive k direction, this means that the object will rotate counterclockwise around the point (5,5). The direction of the torque can also be confirmed by using the right hand rule, where the fingers of the right hand point in the direction of the first vector (r-r0) and curl towards the direction of the second vector (F), giving a positive k direction.

In summary, to find the torque about a specific point, we use the same formula as before but we need to take into consideration the distance between the axis and the point of rotation. The direction of the torque can also be determined using the right hand rule.
 

Related to Finding torque (vector cross product)

1. What is torque?

Torque is a measure of the rotational force applied to an object. It is the product of the force applied to an object and the distance from the axis of rotation.

2. How is torque calculated mathematically?

Torque is calculated by taking the cross product of the force vector and the displacement vector from the axis of rotation. This can be expressed mathematically as T = r x F, where T is torque, r is the displacement vector, and F is the force vector.

3. What is the unit of measurement for torque?

The unit of measurement for torque is typically Newton-meters (N·m) in the SI system. In the US customary system, it is typically measured in foot-pounds (ft·lb).

4. How does the direction of the force affect torque?

The direction of the force vector relative to the axis of rotation determines the direction of the torque. If the force is perpendicular to the displacement vector, the torque will be at its maximum. If the force is parallel to the displacement vector, the torque will be zero.

5. What is the importance of torque in physics and engineering?

Torque is an important concept in physics and engineering as it helps us understand and predict the rotational motion of objects. It is used in the design of machines, engines, and other mechanical systems. It is also a key factor in determining the stability and balance of structures.

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