# Rotational Work & Energy problem

• colton4286
In summary, the question asks to calculate the kinetic energy of the Earth due to its rotation and motion around the sun. Given the assumptions of a uniform sphere and circular orbit, the information needed to solve the problem can be found. The time period of Earth's rotation, mass of the Earth, and moment of inertia of a spherical body are key factors in solving the equation.
colton4286
The Question:

Calculate the kinetic energy (KE) that the Earth has because of (a) its rotation about its own axis and (b) its motion around the sun. Assume that the Earth is a uniform sphere and that its path arond the sun is circular. For comparison, the total energy used in the U.S. in one year is about 9.3 X 10^19 J.

I know that the KE of a rigid object is 1/2*(moment of inertia)*(angular vel.)^2 but how to go solve for KE w/o given any of this info?

colton4286 said:
The Question:

Calculate the kinetic energy (KE) that the Earth has because of (a) its rotation about its own axis and (b) its motion around the sun. Assume that the Earth is a uniform sphere and that its path arond the sun is circular. For comparison, the total energy used in the U.S. in one year is about 9.3 X 10^19 J.

I know that the KE of a rigid object is 1/2*(moment of inertia)*(angular vel.)^2 but how to go solve for KE w/o given any of this info?
Hi colton and welcome to PF,

You are given sufficient information to answer this problem, perhaps the only thing that is missing is the mass of the earth, but we can look that up. Let's start with (a), just the rotation about it's own axis. The question states that we can assume that the Earth is a uniform sphere, so what is the moment of inertia of a sphere about it's own axis?

We also know (or can work out very easily) the angular velocity of the Earth since we know it's period of rotation.

For future reference we have the https://www.physicsforums.com/forumdisplay.php?f=152" specifically for such questions. A moderator will move this thread there shortly so there's no need to start a new thread in there now.

Last edited by a moderator:
the following questions to yourself shall help a great deal::

What is the time period expression for a rotating body?
Now, what is the time period of Earth's rotation about its own axis ?( come on it is a general knowledge question).
Mass of earth= 6 *10^24 kg
What is the moment of inertia of a spherical body?

Kickstart buddy!

## What is rotational work and energy?

Rotational work and energy refers to the physical concept of how rotating objects, such as wheels or gears, can store and transfer energy through rotational motion.

## What is the formula for calculating rotational work?

The formula for calculating rotational work is W = τθ, where W is the work done, τ is the torque applied, and θ is the angular displacement.

## How is rotational work related to rotational kinetic energy?

Rotational work is directly related to rotational kinetic energy. The work done on an object by a torque causes a change in the object's rotational kinetic energy.

## What are some real-life examples of rotational work and energy?

Some examples of rotational work and energy in everyday life include the rotation of car tires, the spinning of a bicycle wheel, and the rotation of wind turbines to produce electricity.

## How can rotational work and energy be applied in engineering and design?

Rotational work and energy are essential concepts in engineering and design, particularly in the fields of mechanics and machinery. Understanding these concepts allows engineers to design and optimize systems that use rotational motion, such as engines, motors, and turbines.

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