A disk-shaped platform has a known rotational inertia ID. The platform is mounted on a fixed axle and rotates in a horizontal plane with an initial angular velocity of ÏD in the counterclockwise direction as shown. After an unknown time interval, the disk comes to rest. A single point on the disk revolves around the center axle hundreds of times before the disk comes to rest. Frictional forces are considered to be constant.

In a different experiment, the original disk is replaced with a disk for which frictional forces are considered to be negligible. The disk is set into motion such that it rotates with a constant angular speed. As the disk spins, a small sphere of clay is dropped onto the disk, and the sphere sticks to the disk.

Required:

Write down the claims which are correct about the angular momentum and the total kinetic energy of the disk-sphere system immediately before and immediately after the collision.

The angular momentum of that same disk-sphere remains unchanged the very same way before and after the impact of the collision when the clay sphere adheres to the disk.

[tex]\mathbf{I_w}[/tex] = constant.

The overall value of such moment of inertia is now altered when the clay spherical sticks. Due to the inclusion of the clay sphere, the moment of inertia will essentially rise. As a result of this increase, the angular speed w decreases in value.

Recall that:

The Kinetic energy is given by:

[tex]\mathbf{K = \dfrac{1}{2} Iw^2} \\ \\\mathbf{K = \dfrac{1}{2} lw*w}[/tex]

where;

[tex]\mathbf{I_w}[/tex] is constant and w reduces;

As a result, just after the collision, the system's total kinetic energy decreases.

shubhamchouhanvrVT shubhamchouhanvrVT · Answer 2 · 2022-03-30T07:31:45+02:00

The total kinetic energy of the system decreases after the collision.

What is angular momentum?

The angular momentum of any rotating body is defined as the product of the moment of inertia of the body and the angular velocity of the body.

Now from the question, we can see that the angular momentum of the body remains constant before and after the impact of the collision when the clay sphere adheres to the disk.

So angular momentum will be

[tex]Iw[/tex] = constant.

The overall value of such a moment of inertia is now changed when the clay spherical sticks. Due to the inclusion of the clay sphere, the moment of inertia will essentially rise. As a result of this increase, the angular speed w decreases in value.

The Kinetic energy is given by:

[tex]KE=\dfrac{1}{2} Iw^2[/tex]

[tex]KE= \dfrac{1}{2} Iw\times w[/tex]

Since the angular momentum [tex]Iw[/tex] is constant and w is reducing then ultimately the energy of the system is decreasing.

Thus the total kinetic energy of the system decreases after the collision.

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