azizlwl said:You should consider translational motion too.
The formula for calculating the total kinetic energy of a rolling hoop is:
K = 1/2 * I * ω^2 + 1/2 * M * v^2, where K is the total kinetic energy, I is the moment of inertia of the hoop, ω is the angular velocity, M is the mass of the hoop, and v is the linear velocity.
The moment of inertia, I, is a measure of an object's resistance to rotational motion. A larger moment of inertia means that the hoop will require more energy to rotate, resulting in a higher total kinetic energy.
Yes, the total kinetic energy of a rolling hoop can change. It can change if the mass or velocity of the hoop changes, or if there is a change in the surface it is rolling on.
The linear velocity, v, of a rolling hoop is directly proportional to its total kinetic energy. This means that as the linear velocity increases, so does the total kinetic energy of the hoop.
The total kinetic energy, K, of a rolling hoop is directly proportional to the square of its angular velocity, ω. This means that as the angular velocity increases, the total kinetic energy of the hoop also increases at a faster rate.