# Rotational kinetic energy and moment of inertia

• court2011
In summary, rotational kinetic energy is the energy an object has due to its rotation and is dependent on the object's mass, moment of inertia, and angular velocity. It differs from linear kinetic energy, which is related to an object's linear motion and is calculated using the moment of inertia. Moment of inertia is a measure of an object's resistance to rotational motion and is dependent on the object's mass, shape, and distribution of mass. The distribution of mass affects moment of inertia, as objects with more mass concentrated towards the axis of rotation will have a smaller moment of inertia. Rotational kinetic energy is directly proportional to the moment of inertia, meaning that objects with a larger moment of inertia will have a greater amount of rotational kinetic energy compared to
court2011

## Homework Statement

A 16 g CD with a radius of 6.0 cm rotates with an angular speed of 42 rad/s.
(a) What is its kinetic energy?

k=1/2Iw^2

## The Attempt at a Solution

k=1/2(0.016x0.0036)(1764)=0.05 J

Careful. The moment of inertia of a disk is not MR^2. That's the moment of inertia for a hoop, or for a point mass.

ohhh so should i have 1/2mr^2

Yup.

kk sweet thanks! i got it right :)

## 1. What is rotational kinetic energy?

Rotational kinetic energy is the energy an object has due to its rotation. It is dependent on the object's mass, moment of inertia, and angular velocity.

## 2. How does rotational kinetic energy differ from linear kinetic energy?

Rotational kinetic energy is related to an object's rotational motion, while linear kinetic energy is related to an object's linear motion. Rotational kinetic energy is calculated using the moment of inertia, while linear kinetic energy is calculated using an object's mass and velocity.

## 3. What is moment of inertia?

Moment of inertia is a measure of an object's resistance to rotational motion. It is dependent on the object's mass, shape, and distribution of mass.

## 4. How does the distribution of mass affect moment of inertia?

The distribution of mass affects moment of inertia because it determines how the mass is distributed around the axis of rotation. Objects with more mass concentrated towards the axis of rotation will have a smaller moment of inertia compared to objects with mass distributed farther from the axis.

## 5. How is rotational kinetic energy and moment of inertia related?

Rotational kinetic energy is directly proportional to the moment of inertia. This means that objects with a larger moment of inertia will have a greater amount of rotational kinetic energy compared to objects with a smaller moment of inertia, given the same angular velocity.

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