Torque & Equivalent Forces

In summary, when finding the resultant of a force system, which includes three pairs of forces with the same magnitude that are parallel and opposite, it is necessary to calculate the torque at a specific point when adding all the torques together. The torque is a free vector and can be added independent of the coordinate system. The resulting moment (torque) will be in the z-axis if the forces are along the x and y axis, since torque is perpendicular to the plane of the two forces. The textbook is unclear on this topic, so clarification is needed.
  • #1
AngelofMusic
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This is a question about finding the resultant of the force system.

Basically, there is a rigid body with 3 pairs of forces with the same magnitude that are parallel to each other and in opposite directions. (I've attached an example of one of those pairs.) All three pairs are attached at different places on a long beam.

I converted one of the forces in each pair into a force-couple system. That means that each pair now has the forces cancelling each other out, and an additional moment (torque) vector.

(i.e. I moved the vector starting at A to point B, and found the torque of A once it has been moved to point B. Then the two forces cancel out.)

I was just wondering - do I also need to calculate the torque at point B when adding all the torques together? Since the torque is supposed to be a free vector, does that mean that all 3 of the resulting torques (with the pairs of forces in different places) can just be added together?

Also, since the forces are along the x and y axis, and the torques are perpendicular to that plane, would that make the resultant moment (torque) solely in the z-axis, then?

The textbook is incredibly confusing on this topic, and I'd appreciate any clarification!
 

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  • #2
Yes, you do need to calculate the torque at point B when adding all the torques together. The three resulting torques can be added together due to the fact that torque is a free vector and thus independent of the coordinate system. The resultant moment (torque) will be in the z-axis if the forces are along the x and y axis, since torque is perpendicular to the plane of the two forces.
 
  • #3


To find the resultant of a force system, you need to consider both the forces and the torques acting on the rigid body. In this case, you have correctly converted one of the forces in each pair into a force-couple system, meaning that you now have two forces acting on the body and an additional torque vector.

When adding all the torques together, you need to consider the sign of each torque. If the torques are in the same direction (clockwise or counterclockwise), you can simply add them together. However, if they are in opposite directions, you need to subtract them from each other. This will give you the net torque acting on the body.

Since the forces are along the x and y axis, and the torques are perpendicular to that plane, the resultant moment (torque) will indeed be solely in the z-axis. This is because the x and y components of the torques will cancel each other out, leaving only the z component as the net torque.

It is important to note that the torque is a free vector, meaning it can act at any point on the rigid body. Therefore, when calculating the resultant torque, you need to consider the torque at each point where the forces are acting. This will give you the total net torque acting on the body.

In conclusion, to find the resultant of a force system, you need to consider both the forces and the torques acting on the rigid body. The torques can be added or subtracted depending on their direction, and the resultant moment will be solely in the z-axis. It is important to consider the torque at each point where the forces are acting in order to calculate the total net torque.
 

1. What is torque?

Torque is a measure of the force that causes an object to rotate around an axis or pivot point. 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.

2. How is torque related to equivalent forces?

Equivalent forces are two or more forces that have the same effect on an object. Torque is related to equivalent forces because it is the rotational equivalent of linear force. In other words, torque and equivalent forces both cause an object to move in a rotational motion.

3. What are the units of torque?

The units of torque are typically measured in newton-meters (Nm) or foot-pounds (ft-lb). These units represent the amount of force required to rotate an object one meter or one foot, respectively.

4. How does the direction of torque affect an object?

The direction of torque determines the direction of the rotational motion of an object. If the torque is applied in a clockwise direction, the object will rotate clockwise. If the torque is applied in a counterclockwise direction, the object will rotate counterclockwise.

5. What factors affect the torque on an object?

The torque on an object is affected by the amount of force applied, the distance from the axis of rotation to the point where the force is applied, and the angle at which the force is applied. The greater the force, the larger the torque. The longer the distance from the axis of rotation, the greater the torque. And the more perpendicular the force is to the axis of rotation, the greater the torque.

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