What is the new position vector if the reference point is changed to (0,4)?

In summary, the particle is located at position (1, 3) m with respect to the origin and is experiencing a force of (5, 6) N. The torque about the origin can be calculated using the cross product of the two vectors (1, 3, 0) and (5, 6, 0). To find the torque about the point (0, 4) m, the position vector must be calculated with respect to that point by adding the new reference point (0, 4) to the original position vector (1, 3). The torque is always calculated with respect to a specific point in the z = 0 plane.
  • #1
tmgrich
1
0
A particle is located at the vector position r = (i + 3 j) m, and the force acting on it is F = (5 i + 6 j) N.
(a) What is the torque about the origin?
(b) What is the torque about the point having coordinates (0, 4) m?

when you are given an i + j, do you assume that it starts at the origin?
then to you add 4 to the j vector since you are changing the point to (0,4)?
 
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  • #2
Torque is defined as the cross product r x F, right?

You're given two vectors: r = (i + 3j) m, and F = (5i + 6j) N.

It sounds to me like you're missing the crucial ingredient that the representation r = (i + 3j) is the same as the "vector notation" (1, 3, 0); the representation (5i + 6j) is the same as (5, 6, 0). Can you calculate the vector cross product of those two vectors?

- Warren
 
  • #3
Use matrix
 
  • #4
tmgrich said:
when you are given an i + j, do you assume that it starts at the origin?
Yes, assume that the "position vector" is with respect to the origin (0,0,0).
then to you add 4 to the j vector since you are changing the point to (0,4)?
Since torque is always calculated with respect to (wrt) some point*, when you change that point from (0,0) to (0,4) you must use a new position vector with respect to that new reference point:
Let A = position of particle wrt 0,0 = 1,3
Let B = position of new reference point wrt 0,0 = 0,4
Let C = position of particle wrt 0,4 = ?
You know that A = B + C, so figure out the new position vector C.

*assumed to be in the z = 0 plane in this problem
 

What is a vector product?

A vector product, also known as a cross product, is a mathematical operation that results in a vector quantity. It is calculated by taking the cross product of two vectors and the magnitude of the resulting vector is equal to the product of the magnitudes of the two original vectors multiplied by the sine of the angle between them.

How is the direction of a vector product determined?

The direction of a vector product is determined by using the right-hand rule. This rule states that if you point your right thumb in the direction of the first vector and your fingers in the direction of the second vector, then the direction of the resulting vector will be perpendicular to both the first and second vectors.

What is torque?

Torque is a measure of the force that can cause an object to rotate around an axis. It is calculated by multiplying the force applied to an object by the distance from the axis of rotation to the point where the force is applied. Torque is measured in units of Newton-meters (Nm) in the SI system.

How does torque affect the motion of an object?

Torque can cause an object to rotate around an axis, either in a clockwise or counterclockwise direction. The direction of the rotation is determined by the direction of the applied force and the direction of the axis of rotation. The magnitude of the torque determines the rate of rotation, with a larger torque resulting in a faster rotation.

What are some common applications of vector products and torque in science?

Vector products and torque have many applications in science, particularly in physics and engineering. They are commonly used to calculate the forces acting on objects, such as in mechanics and structural analysis. They are also used in electromagnetism to calculate the magnetic field produced by a current-carrying wire. In biology, torque is important in understanding the movement of muscles and joints in the human body.

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