To understand how to use conservation of angular momentum to solve problems invo

Question

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 I_t rotating at a constant angular velocity omega_i (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. 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 I_T. The initial angular velocity of the second disk is zero. There is friction between the two disks. After this "rotational collision" the disks will eventually rotate with the same angular velocity. What is the final angular velocity, omega_f, of the two disks? Express omega_f (omega subscript f) Because of friction, rotational kinetic energy is not conserved while the disks' surfaces slip over each other. What is the final rotational kinetic energy. K_f, of the two spinning disks? Express the final kinetic energy in terms of I_t, I_r, and the initial kinetic energy K_j, of the two-disk system. No angular velocities should appear in your answer.

Explanation / Answer

Here , let the final angular speed is f

Using conservation of angular momentum

(It + Ir) * f = It * i

solving for f

f = It * i/(It + Ir)

the final angular speed is It * i/(It + Ir).

part B)

final kinetic energy = 0.5 * If * wf^2

final kinetic energy = 0.5 * (It + Ir) * (It * i/(It + Ir))^2

final kinetic energy = 0.5 *(It * i)^2/(It + Ir)

the final kinetic energy is 0.5 *(It * i)^2/(It + Ir)

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