A solid disk rotates in the horizontal plane at an angular velocity of 0.072 rad

Question

A solid disk rotates in the horizontal plane at an angular velocity of 0.072 rad/s with respect to an axis perpendicular to the disk at its center. The moment of inertia of the disk is 0.078 kg·m2. From above, sand is dropped straight down onto this rotating disk, so that a thin uniform ring of sand is formed at a distance 0.44 m from the axis. The sand in the ring has a mass of 0.67 kg. After all the sand is in place, what is the angular velocity of the disk?

A hoop, a solid cylinder, a spherical shell, and a solid sphere are placed at rest at the top of an incline. All the objects have the same radius. They are then released at the same time. What is the order in which they reach the bottom (fastest first)?

Explanation / Answer

Moi of hoop = mr^2

Moi of solid cylinder = 0.5mr^2

Moi of spherical shell = 0.66mr^2

Moi of inertia of solid sphere = 0.4mr^2

Torque = I × angular acceleration

More the object will have moment of inertia more soon it will reach the ground.

Order = hoop , spherical shell , solid cylinder , solid cylinder

Hoop will reach first and solid sphere will reach at the last.

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