Need a list on derivatives in Physics

In summary, derivatives have a significant interrelation with physics, as they were originally invented to express the concept of "change" in relation to time. However, they have also been applied to other aspects of physics, such as electric fields, showing the versatile nature of the derivative concept.
  • #1
Noone1982
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For a school project, I am trying to compile a good sized list of the interelation of derivatives in physics. I know I can just go through every page in my book but does anyone know any handy links off hand?
 
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  • #2
You mean, the derivative of a function, as in calculus ?

If it's that, know that the mathematical concept of derivative was essentially invented to express a certain concept in physics: "change". Newton and Leibniz are considered to be its inventors.
"change of position with time" = velocity
Newton needed to write down velocity as a function of time, when he had position as a function of time. Hence his definition of velocity v = dx /dt

"change of velocity with time" = acceleration, a = dv/dt = d^2 x/dt^2

Acceleration is the second derivative wrt time, of position.

Newton needed that, to write his famous law: mass x acceleration = force

But the concept of derivative got also used in other ways. For instance, the ELECTRIC FIELD is (minus) the change of potential with position:
E_x = - dV/dx

Note that we now have a derivative towards space, not towards time. So the derivative concept is used further than just "change in time".

In modern physics, derivatives abound, in many ways...
 
  • #3


Sure, here is a list of some common derivatives in physics:

1. Velocity - The derivative of position with respect to time, representing the rate of change of an object's position.

2. Acceleration - The derivative of velocity with respect to time, representing the rate of change of an object's velocity.

3. Force - The derivative of momentum with respect to time, representing the rate of change of an object's momentum.

4. Energy - The derivative of work with respect to distance, representing the rate of change of an object's energy.

5. Power - The derivative of work with respect to time, representing the rate of change of an object's power.

6. Electric field - The derivative of electric potential with respect to distance, representing the rate of change of an object's electric field.

7. Magnetic field - The derivative of magnetic flux with respect to time, representing the rate of change of an object's magnetic field.

8. Pressure - The derivative of force with respect to area, representing the rate of change of an object's pressure.

9. Temperature - The derivative of internal energy with respect to entropy, representing the rate of change of an object's temperature.

10. Density - The derivative of mass with respect to volume, representing the rate of change of an object's density.

Here are some additional resources that may be helpful in your project:

- Khan Academy has a series of videos on derivatives in physics: https://www.khanacademy.org/science...lacement-velocity-time/a/what-are-derivatives

- The Physics Classroom has a comprehensive lesson on derivatives and their applications in physics: https://www.physicsclassroom.com/class/1DKin/Lesson-6/Derivatives-and-Their-Applications

- The University of Illinois at Urbana-Champaign has a list of common derivatives used in physics equations: https://courses.physics.illinois.edu/phys211/old/derivatives.pdf

- The American Institute of Physics has a database of physics equations and their derivatives: https://www.aip.org/sites/default/files/history/teaching-with-history/resources/derivatives.pdf

Hope this helps with your project!
 

1. What is a derivative in physics?

A derivative in physics is a mathematical concept that represents the rate of change of a physical quantity with respect to another quantity. It is a fundamental tool in studying and understanding the behavior of physical systems.

2. How is a derivative calculated in physics?

A derivative in physics is calculated using the rules of calculus, specifically the derivative and chain rule. This involves finding the slope of a curve at a specific point by taking the limit of the ratio of change in the dependent variable to the change in the independent variable.

3. What is the significance of derivatives in physics?

Derivatives in physics are significant as they allow us to describe and analyze the behavior of physical systems in terms of their rates of change. They are also essential in predicting future outcomes and understanding the relationships between different physical quantities.

4. What are some common applications of derivatives in physics?

Some common applications of derivatives in physics include studying the motion of objects, analyzing the behavior of electric and magnetic fields, and understanding the behavior of fluids and gases.

5. How can derivatives be used to solve problems in physics?

Derivatives can be used to solve problems in physics by providing a mathematical framework for describing and predicting the behavior of physical systems. They allow us to model real-world phenomena and make predictions about future outcomes based on the principles of calculus.

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