How do you find torque for a particle at a specific point using vector products?

In summary, the conversation discusses solving for the torque of a particle located at a specific vector position, given a force acting on it. The first part of the problem is solved, but there is confusion about how to approach the second part. The solution involves finding a new vector by subtracting the given coordinates from the original vector, resulting in a torque of 8 nm.
  • #1
Sheneron
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0
[SOLVED] Vector products and torque

Homework Statement


A particle is located at the vector position r = (i + 3j) m, and the force acting on it is F = (1i + 7j) N.
(a) What is the torque about the origin?
(b) What is the torque about the point having coordinates (0, 4) m?

The Attempt at a Solution


I got the answer for the first part, but I am confused about part b. At first I thought I was supposed to just switch (i +3j) with (0,4) but that is not right. So then I thought that maybe I was supposed to do this:
(1,3) - (0,4) = new vector, and the coordinates for the new vector to find the torque which would be equal to 8 nm. Is that how I am supposed to do it?
 
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  • #2
Quite correct.
 
  • #3
I thank ye
 

1. What is a vector product?

A vector product, also known as a cross product, is a mathematical operation that combines two vectors to produce a third vector that is perpendicular to both of the original vectors. It is represented by the symbol "x" and is commonly used in physics and engineering to calculate torque.

2. How is torque related to vector products?

Torque is the measure of a force's ability to rotate an object around an axis. It is calculated by multiplying the magnitude of the force by the distance from the axis to the point of application. Vector products are used to determine the direction of the torque, as torque is a vector quantity.

3. What is the difference between a scalar and a vector quantity?

A scalar quantity is a measurement that only has magnitude, such as temperature or mass. A vector quantity has both magnitude and direction, such as velocity or force. Torque is an example of a vector quantity as it has both magnitude and direction.

4. How do you calculate the magnitude of a vector product?

The magnitude of a vector product is equal to the product of the magnitudes of the two vectors multiplied by the sine of the angle between them. It can also be calculated using the determinant of a matrix. The magnitude of a vector product is always a positive value.

5. What are some real-world applications of vector products and torque?

Vector products and torque are used in various fields such as mechanics, engineering, and physics. Some common applications include calculating the torque needed to rotate a wheel, determining the forces acting on a lever, and analyzing the motion of objects in a magnetic field.

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