What is the relationship between Torque and Energy?

[Rising_Hg]

I was reading about Torque on Wikipedia (http://en.wikipedia.org/wiki/Torque" ).

There was this relation given :

Energy = Torque * Angle covered.
Can anybody explain me how or show the derivation ?

- Rising_Hg

 

[dacruick]

i didnt even know that relation existed but i can give it a shot.

Energy is force x distance. So you have torque, which is force multiplied by radius. radius multiplied by angle covered is going to be a distance. So there is force x distance. which is energy.

 

[Redbelly98]

i didnt even know that relation existed but i can give it a shot.

Yep, that's it.

 

[uart]

Perhaps the OP is not familiar with radian angle measurement. Is this the case Rising_Hg?

 

[PJC01]

The relationship between torque and energy can be explained through the concept of work. Torque is a measure of the rotational force applied to an object, while energy is the ability to do work. In other words, torque is the cause and energy is the effect.

The formula given, E = T * θ, shows that the energy produced by a torque is directly proportional to the magnitude of the torque and the angle through which it is applied. This can be derived from the equation for work, W = F * d * cosθ, where F is the force applied, d is the distance over which the force is applied, and θ is the angle between the force and the displacement.

In rotational motion, the force is replaced by torque, and the distance is replaced by the angle of rotation. Thus, the equation becomes W = T * θ * cosθ. Since cosθ is equal to 1 when θ is 0, the equation reduces to W = T * θ. This is the same as the relationship given between energy and torque.

In simpler terms, when a torque is applied to an object, it causes it to rotate through a certain angle. This rotation requires energy, and the amount of energy produced is directly proportional to the torque applied and the angle through which it is applied. Therefore, the relationship between torque and energy is that torque results in the production of energy, which can be measured by the amount of work done in rotating an object.