Why is Fty positive in the Σtorque equation?

In summary, the conversation discusses the sign of torque and how it is determined by the direction of the force generating it. The person is having trouble understanding why Fty is positive in the ΣTorque equation, but it is explained that because Fty is up, it generates a counterclockwise or positive torque about the hinge. This is further clarified by considering the direction of the force and its effect on the system's rotation.
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guyvsdcsniper
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Homework Statement
Problem 12.3 A uniform beam, 2.20 m long with mass m = 25.0 kg, is mounted by a small hinge on a wall as shown in the figure The beam is held in a horizontal position by a cable that makes an angle 0 = 30.0° . The beam supports a sign of mass M = 28.0 kg suspended from Store its end. Determine the components of the force h that the (smooth) hinge exerts on the beam, and the tension FT in the supporting cable.
Relevant Equations
ΣT=0
I am reviewing this problem from my textbook and am having some trouble with it. When solving for ΣTorque I chose the hinge to be the axis of rotation. I understand that from this point if the board is being held up and it were to fall after removing support, mg (the center of mass of the board) would fall in the clockwise direction making it negative, Mg (the sign/end of the board) would fall in the clockwise direction making it negative as well. What is confusing me is how Fty is positive/being added to the Σtorque equation. For a visual, please refer to the "alternate solution" section at the bottom of this image. This is how my professor approached this problem and was hoping someone could explain why Fty is positive? Is it because it is being supported by FT?

Screen Shot 2021-04-05 at 7.22.21 PM.png
 
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The way I prefer to think about the sign of a particular torque is to say to myself, "If the force that is generating it were the only force acting on the system, will the system rotate clockwise or counterclockwise?" Here FTy is up, therefore the torque it generates about the hinge is counterclockwise or positive.
 
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kuruman said:
The way I prefer to think about the sign of a particular torque is to say to myself, "If the force that is generating it were the only force acting on the system, will the system rotate clockwise or counterclockwise?" Here FTy is up, therefore the torque it generates about the hinge is counterclockwise or positive.
That makes sense! Didnt think about Fty being up. I missed that. Thank you!
 

1. Why is Fty positive in the Σtorque equation?

Fty refers to the tangential component of force, which is the force that acts perpendicular to the radius of rotation. In the Σtorque equation, this force is positive because it is in the same direction as the angular acceleration, which is also positive. This means that the force is causing an increase in the rotation or angular velocity.

2. Can Fty ever be negative in the Σtorque equation?

Yes, Fty can be negative in the Σtorque equation. This would occur when the tangential force is acting in the opposite direction of the angular acceleration. This would result in a decrease in the rotation or angular velocity.

3. How does Fty affect the overall torque?

Fty is just one component of the overall torque equation, which also includes the radial component of force (Frx) and the radius of rotation (r). The tangential force (Fty) affects the torque by contributing to the overall force acting on the object, which in turn affects the angular acceleration and rotation.

4. Is Fty the only force that can cause torque?

No, Fty is not the only force that can cause torque. As mentioned before, there is also the radial component of force (Frx) and the radius of rotation (r) that contribute to the overall torque. In addition, any force that acts at a distance from the axis of rotation can also cause torque.

5. How is Fty related to the concept of angular momentum?

Fty is related to angular momentum in that it is one of the factors that can affect the angular acceleration and therefore the angular velocity. The concept of angular momentum is based on the idea that an object's rotational motion is affected by both its mass and its distribution of mass. Fty is one of the forces that can contribute to this distribution of mass and therefore affect the object's angular momentum.

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