What is the Moment Produced by a Force at the Origin?

In summary, the moment of a force is a measure of its tendency to cause rotation, while the cross product of two vectors is a vector perpendicular to both original vectors with a magnitude equal to the product of their lengths multiplied by the sine of the angle between them. The moment of a force is calculated by taking the cross product of the force and position vectors. The right-hand rule is used to determine the direction of the resulting vector in cross product calculations. The cross product can be zero if the vectors are parallel or if one vector has a magnitude of zero. In physics and engineering, it is used to calculate moments of forces, determine torque direction, solve problems involving rotational motion, and in vector calculus and electromagnetism to calculate magnetic fields.
  • #1
khutch2212
4
0
F = 5i + 3j Newtons acts 3 m to the right of the origin (x is horizontal and y is vertical). What moment does this force produce about the origin? Use the vector cross product.
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  • #2
OK, show us what you have tried.
 
  • #3
I really don't know where to start, b/c I don't understand how I am suppost to use the cross product with one vector.
 
  • #4
Who says you have only one vector? Remember, a vector has magnitude and direction.
 
  • #5
Does this help?

[itex]\bar{M}_{o} = \bar{R}[/itex] X [itex]\bar{F}[/itex]
 

FAQ: What is the Moment Produced by a Force at the Origin?

What is the difference between moment and cross product?

The moment of a force is a measure of its tendency to cause rotation around a specific point. On the other hand, the cross product of two vectors is a vector that is perpendicular to both of the original vectors and has a magnitude equal to the product of their lengths multiplied by the sine of the angle between them.

How is the moment of a force calculated?

The moment of a force can be calculated by taking the cross product of the force vector and the position vector of the point of rotation. This results in a vector that represents the magnitude and direction of the moment.

What is the right-hand rule and how is it used in cross product calculations?

The right-hand rule is a way to determine the direction of the resulting vector in a cross product calculation. It states that when the fingers of the right hand curl in the direction from the first vector to the second vector, the thumb will point in the direction of the resulting vector.

Can the cross product of two vectors be zero?

Yes, the cross product of two vectors can be zero if the vectors are parallel or if one of the vectors has a magnitude of zero.

How is the cross product used in physics and engineering?

The cross product is used in physics and engineering to calculate moments of forces, determine the direction of torque, and solve problems involving rotational motion. It is also used in vector calculus and electromagnetism to calculate magnetic fields.

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