# Why is Fty positive in the Σtorque equation?

• guyvsdcsniper
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.

#### guyvsdcsniper

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?

Delta2
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.

guyvsdcsniper
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. What is net torque?

Net torque is the measure of the combined rotational force acting on an object. It is the product of the force applied and the distance from the axis of rotation.

## 2. What are the components of net torque?

The components of net torque are the magnitude of the force, the distance from the axis of rotation, and the angle between the force and the lever arm.

## 3. How do you calculate net torque?

To calculate net torque, you need to multiply the magnitude of the force by the distance from the axis of rotation and the sine of the angle between the force and the lever arm.

## 4. How does the direction of the force affect net torque?

The direction of the force affects net torque by changing the angle between the force and the lever arm. A force applied perpendicular to the lever arm will have a greater effect on net torque than a force applied parallel to the lever arm.

## 5. What is the unit of measurement for net torque?

The unit of measurement for net torque is Newton-meters (Nm) in the SI system. In the imperial system, it is measured in foot-pounds (ft-lb).