# Moment of forces about the axes

• Engineering
• mingyz0403
In summary, to determine the sign of Ma and Mb for their y and z component, use the right-hand rule to find the direction of the moment vector and then determine the projection and signage of the vector components onto the y and z axes. The A-torque is negative when looked at in the +y direction, while the B-torque is positive when looked at in the +y direction. The couple about the x-axis is negative because it points in the negative x direction.
mingyz0403
Homework Statement
Shafts A and B connect the gear box to the wheel assemblies of a tractor, and shaft C connects it to the engine. Shafts A and B lie in the vertical yz plane, while shaft C is directed along the x axis. Replace the couples applied to the shafts by a single equivalent couple, specifying its magnitude and the direction of its axis.
Relevant Equations
M=RXF
I reslove Ma and Mb into y and z component.
Ma=1200sin(20)j+1200cos(20)k
Mb=900sin(20)j+1200cos(20)k
Mc=-840i

I looked at the solution and it states that the y component of Ma is negative (-1200sin(20)j+1200cos(20)k). I understand that Mc is -840i because it is Clockwise. How do you determine the sign of Ma and Mb for their y and z component.

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It is best to forget about sign conventions for clockwise and counterclockwise. Rather, show the couple in its vector form using the right hand rule , and the moment vector will point in the direction of your thumb. Then you should be able to more easily find the projection and signage of the vector Components onto the y and z axes. Hint: the couple about the x-axis is negative because it points in the negative x direction.

FactChecker
The A-torque is tilted slightly down, in the -y direction. Using the right-hand rule, it is positive when looked at in the -y direction. That is the same as negative in the +y direction. The B-torque is tilted slightly up in the +y direction.

## 1. What is a moment of force?

A moment of force, also known as torque, is the measure of the tendency of a force to rotate an object about an axis. It is calculated by multiplying the force by the perpendicular distance from the axis of rotation to the line of action of the force.

## 2. What are the different types of moments of force?

There are two types of moments of force: clockwise and counterclockwise. A clockwise moment of force causes an object to rotate in a clockwise direction, while a counterclockwise moment of force causes an object to rotate in a counterclockwise direction.

## 3. How is the moment of force calculated?

The moment of force is calculated by multiplying the force vector by the perpendicular distance from the axis of rotation to the line of action of the force. This can be represented by the formula: M = F x d, where M is the moment of force, F is the force vector, and d is the distance from the axis of rotation to the line of action of the force.

## 4. What is the importance of moments of force in physics?

Moments of force are important in physics because they play a crucial role in understanding the motion and stability of objects. They are used to describe the rotational motion of objects and are essential in engineering and design applications, such as building structures and machines.

## 5. How do moments of force affect the equilibrium of an object?

Moments of force can cause an object to be in equilibrium, meaning that it is not moving or rotating. This occurs when the sum of all the clockwise moments equals the sum of all the counterclockwise moments. If the moments are not balanced, the object will experience a rotational motion.

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