Angular equivalent of energy?

In the case of linear motion, the energy is kinetic energy, while in the case of angular motion, it is rotational kinetic energy.
  • #1
neuralnova
6
0
Many linear quantities have angular counterparts.

Mass --> Moment of inertia
velocity --> angular velocity
acceleration --> angular acceleration
force --> torque
momentum --> angular momentum

E = mc^2 --> ? = I ?^2

Even a loose analogy would do.
 
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  • #2
Welcome to PF!

Linear kinetic energy -> rotational kinetic energy
 
  • #3
Or mathematically, ##\frac{1}{2}mv^2 \rightarrow \frac{1}{2} I \omega^2##.
 
  • #4
Sure -- I should have included those in my list, as I did already know about them. I'm looking for something more daring. ;)
 
  • #5
neuralnova said:
I'm looking for something more daring.
mc^2 is not related to linear or angular motion, so I'm not sure in what sense there can be an "angular counterpart".
 
  • #6
Energy isn't linear by default, it's a more general concept that can be applied to both linear and angular motion.
 

1. What is the Angular equivalent of energy?

The Angular equivalent of energy is called angular momentum. It is a measure of an object's rotational motion and is defined as the product of its moment of inertia and its angular velocity.

2. How is angular momentum related to energy?

Angular momentum is related to energy through the principle of conservation of angular momentum. This states that in a closed system, the total angular momentum remains constant, meaning that any changes in one object's angular momentum must be balanced by an equal and opposite change in another object's angular momentum.

3. How is angular momentum calculated?

The formula for calculating angular momentum is L = I * ω, where L is the angular momentum, I is the moment of inertia, and ω (omega) is the angular velocity. The moment of inertia depends on the mass and distribution of mass of the object, while the angular velocity is the rate at which the object rotates.

4. How is angular momentum measured?

Angular momentum is measured in units of kilogram meters squared per second (kg·m2/s). This is derived from the formula for angular momentum, where the units for moment of inertia are kg·m2 and the units for angular velocity are 1/s.

5. What are some real-world examples of angular momentum?

Some examples of angular momentum in everyday life include a spinning top, a rotating bicycle wheel, a figure skater performing a spin, and a planet orbiting around a star. It is also important in the design of vehicles and machines that involve rotational motion, such as helicopters and wind turbines.

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