Question

Disk rotating about its center and attached to a torsional spring. (Kinetics and Energy Methods) Solution: 5mRzë + kże = 0,wn = akt mR2 m, Jo KE o R

Answer 1

The moment of inertia of the system can be calculated using the equation I = Σ mjr². The rotational kinetic energy can be found using the equation K = 1/2 Iω².

Step-by-step explanation:

The moment of inertia of a system is a measure of its resistance to changes in rotational motion. In this question, the moment of inertia can be calculated using the equation I = Σ mjr², where m is the mass and r is the radius. To find the rotational kinetic energy, the equation K = 1/2 Iω² can be used, where I is the moment of inertia and ω is the angular velocity.

1. (a) To find the moment of inertia of the system, we need to calculate the moment of inertia of the disk and the annular cylinder separately and then add them together. The moment of inertia of a disk is given by 1/2 mR², where m is the mass and R is the radius. The moment of inertia of the annular cylinder can be found using the equation for the moment of inertia of a thin-walled hollow cylinder, which is (1/2)m(R₁² + R₂²), where R₁ and R₂ are the inner and outer radii, respectively.
2. (b) To find the rotational kinetic energy, we can substitute the moment of inertia and the angular velocity into the equation K = 1/2 Iω².