a solid disk rotates in the horizontal plane

When a solid disk rotates in the horizontal plane, its angular momentum is conserved. The angular momentum is a vector quantity that represents the momentum of rotation of an object.

If the solid disk is rotating without any external torque acting on it, then its angular momentum will remain constant. This means that the product of its moment of inertia, rotational speed, and radius will remain the same.

The moment of inertia of a solid disk is given by:

I = (1/2) * m * r^2,

where m is the mass of the disk and r is its radius. The rotational speed of the disk is given by its angular velocity, denoted by the Greek letter omega (ω).

Therefore, the angular momentum of the disk is:

L = I * ω = (1/2) * m * r^2 * ω.

As the disk rotates, its kinetic energy is also conserved, given by:

K = (1/2) * I * ω^2 = (1/4) * m * r^2 * ω^2.

Thus, the speed of the rotating disk can be determined from its moment of inertia, rotational speed, and kinetic energy.