Learning Goal: To understand how to use conservation of angular momentum to solve problems involving collisions of rotating bodies. Consider a turntable to be a circular disk of moment of inertia It rotating at a constant angular velocity ωi(note that angular velocities use the Greek letter omega and not double-u) around an axis through the center and perpendicular to the plane of the disk (the disk's "primary axis of symmetry") as shown in (Figure 1). The axis of the disk is vertical and the disk is supported by frictionless bearings. The motor of the turntable is off, so there is no external torque being applied to the axis. Another disk (a record) is dropped onto the first such that it lands coaxially (the axes coincide). The moment of inertia of the record is Ir There is friction between the two disks. After this "rotational collision," the disks will eventually rotate with the same angular velocity. a)What is the final angular velocity, ωf Express ωf (omega subscript f) in terms of It Ir ωi (omega subscript i).   b)Because of friction, rotational kinetic energy is not conserved while the disks' surfaces slip over each other. What is the final rotational kinetic energy, Kf Express the final kinetic energy in terms of It Ir Ki of the two-disk system. No angular velocities should appear in your answer.

College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Learning Goal:

To understand how to use conservation of angular momentum to solve problems involving collisions of rotating bodies.

Consider a turntable to be a circular disk of moment of inertia It rotating at a constant angular velocity ωi(note that angular velocities use the Greek letter omega and not double-u) around an axis through the center and perpendicular to the plane of the disk (the disk's "primary axis of symmetry") as shown in (Figure 1). The axis of the disk is vertical and the disk is supported by frictionless bearings. The motor of the turntable is off, so there is no external torque being applied to the axis.

Another disk (a record) is dropped onto the first such that it lands coaxially (the axes coincide). The moment of inertia of the record is Ir

There is friction between the two disks.

After this "rotational collision," the disks will eventually rotate with the same angular velocity.

a)What is the final angular velocity, ωf

Express ωf (omega subscript f) in terms of It Ir ωi (omega subscript i).
 
b)Because of friction, rotational kinetic energy is not conserved while the disks' surfaces slip over each other. What is the final rotational kinetic energy, Kf
Express the final kinetic energy in terms of It Ir Ki of the two-disk system. No angular velocities should appear in your answer.
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