Two disks are mounted (like a merry-go-round) on low-friction bearings on the same axle and can be brought together so that they
couple and rotate as one unit. The first disk, with rotational inertia 2.11 kg·m2 about its central axis, is set spinning counterclockwise (which may be taken as the positive direction) at 372 rev/min. The second disk, with rotational inertia 8.41 kg·m2 about its central axis, is set spinning counterclockwise at 631 rev/min. They then couple together. (a) What is their angular speed after coupling? If instead the second disk is set spinning clockwise at 631 rev/min, what are their (b) angular velocity (using the correct sign for direction) and (c) direction of rotation after they couple together?
1 answer:
Since no external torque is acting on the system you can use the conservation of angular momentum. I derived the final angular speed below and shown my work on how I did it. It’s now just a matter of plugging in the numbers and using correct placement of negative sign for direction of angular velocity. L in the picture stands for angular momentum. Hope it helps
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Answer:
(a):
(b):
(c):
Explanation:
Given that an electron revolves around the hydrogen atom in a circular orbit of radius r = 0.053 nm = 0.053 m.
Part (a):
According to Coulomb's law, the magnitude of the electrostatic force of interaction between two charged particles of charges and
respectively is given by
where,
= Coulomb's constant =
= distance of separation between the charges.
For the given system,
The Hydrogen atom consists of a single proton, therefore, the charge on the Hydrogen atom,
The charge on the electron,
These two are separated by the distance,
Thus, the magnitude of the electrostatic force of attraction between the electron and the proton is given by
Part (b):
The gravitational force of attraction between two objects of masses and
respectively is given by
where,
= Universal Gravitational constant =
For the given system,
The mass of proton,
The mass of the electron,
Distance between the two,
Thus, the magnitude of the gravitational force of attraction between the electron and the proton is given by
The ratio :