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

• warfreak131
In summary, the conversation discusses the application of the energy equation in a lever arm system where the load is attached to a hinge, resulting in a constant downward direction. The question is raised about whether the equation only applies when the angle between the arm and the load is constant. It is clarified that the equation still applies when the angle is changing, but an integral must be taken with the force and angle being expressed in terms of rotation angle phi. The concept of integral is also clarified, and it is mentioned that an online math input platform can be used if needed.
warfreak131
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.

## 1. How do you calculate the energy required via torque when rotating an object?

The energy required via torque can be calculated by multiplying the torque (in units of Newton meters) by the angular displacement (in units of radians). This means that the formula for calculating energy required via torque is E = τθ, where E is the energy required, τ is the torque, and θ is the angular displacement.

## 2. What is the relationship between torque and energy?

Torque and energy are directly proportional to each other. This means that as the torque increases, the energy required to rotate an object also increases. Similarly, if the torque decreases, the energy required will also decrease.

## 3. How does the mass of an object affect the energy required via torque?

The mass of an object does not directly affect the energy required via torque. The energy required is only dependent on the torque and angular displacement, not on the mass of the object. However, the mass of an object can affect the torque needed to rotate it, which in turn will affect the energy required.

## 4. Can you calculate the energy required via torque for non-circular motion?

Yes, the energy required via torque can be calculated for any type of motion, not just circular motion. However, the formula may vary depending on the type of motion and the specific variables involved.

## 5. How do you convert torque from one unit to another?

To convert torque from one unit to another, you can use the conversion factor of 1 Nm = 1 Joule. This means that to convert from Newton meters to Joules, you simply multiply the torque by 1. If you need to convert to a different unit, you can use a conversion table or online converter to determine the appropriate conversion factor.

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