What is the moment about point C?

In summary, the question asks for the moment about the origin of a vector with a magnitude of 100 units, acting from point A=(2, 0, 4) to point B=(5, 1, 1). The solution involves finding the distance from the origin to the line of direction of the vector and from point C=(-1, 2, 1) to that line, and then multiplying those distances by the magnitude of the vector.
  • #1
Angello90
65
0

Homework Statement


Find the moment about the origin of a vector of magnitude 100 units acting from
A=(2, 0, 4) to B=(5, 1, 1). What is the moment about the point C=(−1, 2, 1)?


Homework Equations


M= r x F


The Attempt at a Solution


I did the quesion, but I'm not sure if it's correct. Can anyone check it for me?
attachment.php?attachmentid=25347&d=1272109619.jpg
 

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  • #2
The "moment of a vector about a point" is the magnitude of the vector times the length of a line segment from the given point perpendicular to the line of the vector.

Since the vector acts "from (2, 0, 4) to (5, 1, 1)", its line of direction is given by x= 3t+ 2, y= t, z= -3t+ 4. You need to find the distance from (0, 0, 0) to that line and from (-1, 2, 1) to that line . Then multiply those by 100.
 
  • #3
So I need to find |OL| where O = (0, 0, 0) and L = (2+3t, t, 4-3t), thus
attachment.php?attachmentid=25353&d=1272111831.jpg


Making a moment of
attachment.php?attachmentid=25350&d=1272111706.jpg


Simillary to Q = (-1, 2, 1)
attachment.php?attachmentid=25354&d=1272111831.jpg
 

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  • Mol.jpg
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  • OL.jpg
    OL.jpg
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  • QL Mql.jpg
    QL Mql.jpg
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  • #4
Ahhh come on guys help me out here! Any hints?
 

Related to What is the moment about point C?

What is moment about the origin?

Moment about the origin is a concept in physics and engineering that refers to the measure of the rotational effect of a force around a fixed point or axis, known as the origin. It is also known as torque or moment of force.

How is moment about the origin calculated?

Moment about the origin is calculated by multiplying the magnitude of the force by the perpendicular distance from the origin to the line of action of the force. The unit of moment is Newton-meter (Nm) in the SI system.

What is the importance of moment about the origin?

Moment about the origin is important in analyzing the stability and equilibrium of objects and structures. It is also used in designing and analyzing mechanical systems, such as levers, gears, and pulleys.

What factors affect the moment about the origin?

The moment about the origin is affected by the magnitude of the force, the distance from the origin to the line of action of the force, and the direction of the force. In addition, the point of application of the force can also affect the moment.

Can moment about the origin be negative?

Yes, moment about the origin can be negative if the force and the distance are in opposite directions. A negative moment indicates that the rotational effect of the force is in the opposite direction of the specified axis or point of rotation.

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