# How much rotational kinetic energy does the disk have ?

• IntegrateMe
In summary, a 2.1 kg disk is being pulled with a constant force of 9 N while a string is wrapped around it. The center of mass has moved 0.11 m and the hand has moved 0.28 m. The question asks for the rotational kinetic energy of the disk at this instant, as well as the moment of inertia and the meaning of rotational kinetic energy "relative to the center of mass."
IntegrateMe
A string is wrapped around a disk of mass 2.1 kg (it's density doesn't have to be uniform). From rest, you pull the string with a constant force of 9 N. At this instant, the center of mass has moved 0.11 m, and your hand has moved 0.28 m.

1. At this instant, how much rotational kinetic energy does the disk have relative to its center of mass?

2. At this instant, the angular speed of the disk is 7.5 rads/s. What is the moment of inertia of the disk?

Relevant equations? Attempt at solution? Your thoughts?

Exactly what is meant by rotational kinetic energy "relative to the center of mass"?

## 1. How is rotational kinetic energy defined?

Rotational kinetic energy is the energy an object possesses due to its rotation around an axis. It is calculated by multiplying half of the object's moment of inertia by the square of its angular velocity.

## 2. What factors affect the amount of rotational kinetic energy a disk has?

The amount of rotational kinetic energy a disk has is affected by its moment of inertia, which is dependent on its mass distribution and shape, as well as its angular velocity, which is affected by the speed at which it is rotating.

## 3. How does rotational kinetic energy relate to linear kinetic energy?

Rotational kinetic energy and linear kinetic energy are both forms of kinetic energy, but they are calculated differently. While rotational kinetic energy is based on an object's rotation, linear kinetic energy is based on its linear motion. However, the two energies can be converted into each other using the principle of conservation of energy.

## 4. Can the rotational kinetic energy of a disk be negative?

No, the rotational kinetic energy of a disk cannot be negative. This is because the formula for calculating rotational kinetic energy only involves positive values, and the kinetic energy of an object cannot be negative according to the laws of thermodynamics.

## 5. How can I calculate the rotational kinetic energy of a disk?

To calculate the rotational kinetic energy of a disk, you will need to know its moment of inertia and angular velocity. The formula for rotational kinetic energy is KE = 1/2 * I * ω^2, where KE is the kinetic energy, I is the moment of inertia, and ω is the angular velocity. Simply plug in these values and solve to find the rotational kinetic energy of the disk.

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