# Solving Static Equilibrium: Ʃτ = 0, ƩF = 0

• capn awesome
In summary, the conversation discusses finding the angle ψ using the equations Ʃτ = 0 and ƩF = 0. The solution involves summing the torques for each piece and using the lever equation to find ψ. The conversation also mentions the possibility of checking the solution and the limitations of finding the angle without considering torque.

#### capn awesome

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Ʃτ = 0
ƩF = 0

## The Attempt at a Solution

summing the torques for each piece, i found

Ʃτ = MgLsin(90-ψ) - mgIsin(ψ) = 0

MgLsin(90-ψ) = mgIsin(ψ)

ML/mI = sin(ψ)/sin(90-ψ) = sin(ψ)/cos(-ψ) = tan(ψ)

so ψ = tan-1(ML/mI)

i don't know if this is correct or not...

and I have no idea how I could find the angle without considering torque. any help is appreciated. thanks :)

#### Attachments

• ps1b.gif
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i don't know if this is correct or not...
How could you go about checking it?

and I have no idea how I could find the angle without considering torque.
I don't think you can. But you can do it without directly considering torque by using a result - like the lever equation.

## 1. What is static equilibrium and why is it important?

Static equilibrium is a state in which all forces acting on a body are balanced, resulting in no net acceleration. This is important in physics because it allows us to predict the behavior of objects at rest or in constant motion.

## 2. What is the difference between Ʃτ = 0 and ƩF = 0?

Ʃτ = 0 refers to the sum of all torques acting on an object being equal to zero, while ƩF = 0 refers to the sum of all forces acting on an object being equal to zero. In other words, Ʃτ = 0 deals with rotational equilibrium, while ƩF = 0 deals with translational equilibrium.

## 3. How do you solve for static equilibrium?

To solve for static equilibrium, you must first draw a free body diagram of the object in question, identifying all forces and their directions. Then, apply the equations Ʃτ = 0 and ƩF = 0 to find the unknown forces or torques, making sure to choose a point of rotation and direction of rotation for Ʃτ = 0.

## 4. Can an object be in static equilibrium if it is moving?

No, an object cannot be in static equilibrium if it is moving. Static equilibrium only applies to objects at rest or in constant motion. If an object is experiencing any type of acceleration, it is not in static equilibrium.

## 5. How does solving for static equilibrium apply to real-world situations?

Solving for static equilibrium is important in many real-world situations, such as building structures, bridges, and machines. Engineers and architects use the principles of static equilibrium to ensure that their designs can withstand the forces acting on them without collapsing or breaking.