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33. Problem 13.35 (HRK) A uniform disk of mass M and radius R rotates about a
horizontal axis through its centre with angular speed
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(a) What is its kinetic energy? Its angular momentum? (b) a chip
of mass m breaks off the edge at an instant such that the chip rises vertically
above the point at which it broke off. How high above the point does it rise
before starting to fall? (c) What is the final angular speed of the
broken disk? 
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Solution: Click For PDF Version (a) Rotational inertia of a flat disk of mass M and radius R about
a horizontal axis passing through its centre is
The angular momentum of the disk will be
(b) As the chip of mass m shoots vertically up after it is chipped off the
disk at its rim, its speed at that instant will be
It will go up by height h determined by the conservation of energy. That is
Angular momentum of the chip with respect to the centre of the disk will be its value before it got chipped of the block and will remain constant during its motion. It is
(c) Assuming that the piece of mass m is chipped off from the rim of the
disk, the rotational inertia
Let
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Kinetic
energy of the disk will be 
of the
chipped disk will be
be the
angular speed of the chipped disk. From the conservation of angular momentum, we
have