# Rolling disk, energy before pure rotational?

• kanki
In summary, the conversation discusses the distance traveled by a solid disk with a given angular speed when it is lowered onto a horizontal surface and released, with a specific coefficient of friction. Conservation of momentum is applied to find the work done by friction, which determines the distance traveled before pure rolling occurs. The concept of pure rolling is also defined as when the torque due to friction is less than a certain value, indicating a combination of translational and rotational motion.

#### kanki

Suppose a solid disk of radius R is given an angular speed about an axis through its center and then lowered to a horizontal surface and released, the coefficient of friction between disk and surface is u. What is the distance traveled before pure rolling occurs?

Conservation of Momentum is applied because no net torque.

The work done by the friction of the disk, fx is used to find the distance x travelled. however i do not know which energy has been changed into work done by friction. What is meant by pure rolling? Only translational and rotational? I'm stuck here.

The initial energy of the disc is rotational and is given by -

$$E = \frac{1}{2}I\omega ^2$$

Pure rolling starts when the slipping stops, that is, when the torque due to friction is less than a certain value.

## 1. What is the concept of rolling disk in physics?

The concept of a rolling disk in physics refers to an object that is moving both rotationally and translationally at the same time. This means that the disk is spinning on its own axis while also moving in a straight line.

## 2. How is energy related to pure rotational motion of a disk?

Energy is related to pure rotational motion of a disk through the conservation of energy principle. The kinetic energy of the disk is equal to the sum of its translational kinetic energy and its rotational kinetic energy. This means that as the disk rotates, its energy is conserved and remains constant.

## 3. What is the difference between kinetic energy and potential energy in a rolling disk?

Kinetic energy in a rolling disk refers to the energy of motion, specifically the energy of both rotation and translation. Potential energy, on the other hand, refers to the energy that an object has due to its position or configuration. In a rolling disk, potential energy is converted into kinetic energy as the disk moves.

## 4. How does the moment of inertia affect the energy of a rolling disk?

The moment of inertia, which is a measure of an object's resistance to rotational motion, affects the energy of a rolling disk in that objects with a higher moment of inertia require more energy to rotate at the same speed compared to objects with a lower moment of inertia.

## 5. Can a rolling disk have both kinetic and potential energy?

Yes, a rolling disk can have both kinetic and potential energy. As the disk rolls, it has both rotational and translational kinetic energy. Additionally, if the disk is on an inclined surface, it will also have potential energy due to its position in the gravitational field.