How do you calculate the energy required via torque when....

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To calculate the energy required via torque when dealing with a lever arm and a load, the integral formula Energy = ∫τ dφ applies, where τ = Fr sin(θ). If the angle θ between the arm and the load changes during rotation, both F and θ should be expressed in terms of φ for accurate calculations. When both F and θ are constant, the integral simplifies, eliminating the need for complex calculations. Understanding the integral concept is crucial for proper application in these scenarios. Accurate mathematical representation is essential, and tools like online math input platforms can aid in this process.
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Let's say you have a lever arm connected to a load at the end. But the load is attached to a hinge, so no matter where the lever arm is, the load is always pointing down. I know that Energy = [integral] tau d_phi, but does that only work if the angle b/w arm and load is constant?

What if the angle between the arm and the load, theta, is changing throughout the rotation, phi?
 

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If the angle θ is not constant. We can just take the integral ∫τ·dφ, τ = Frsinθ, with F and θ in terms of φ. If both F and θ are constant than we do not need an integral. I think you might have some misunderstanding about the concept of integral. Also, what do you mean by "load"?
 
The "load" is just my way of saying the force. I understand the integral, I just wasn't sure if it was as easy as dropping in the FrSin[x] into the integral, but I guess it is. Thank you.
 
Another Suggestion. If you do not know Latex, you can search for an online math input platform to enter mathematical expressions.
 

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