A grindstone of mass 13 kg and radius 0.3 m is initially rotating freely at 31 rad/sec. An axe is brought into contact with the grindstone, which brings it to a stop in 8 seconds. Assume the grindstone is a uniform solid cylinder. 1) What is the moment of inertia of the grindstone around its rotation axis?
2) Assuming that the angular acceleration of the grindstone is constant, what is the magnitude of the angular acceleration as it slows to a stop ?
3) Through what angle does the grindstone rotate as it slows to a stop?
4) As the grindstone slows to a stop, mechanical energy is conserved for which of these systems ? The grindstone The grindstone and the axe Mechanical energy is not conserved for either of these systems.
5) As the grindstone slows to a stop, what is the magnitude of the work done on it by the axe? (Hint: Use the work kinetic-energy theorem).
6) Let’s call the magnitude of the work done in this first situation W0. If the grindstone had stopped spinning in half the time, the magnitude of the work done would have been
a) Greater than W0
b) Equal to W0
c) Less than W0
7) If we replace this grindstone with a different grindstone that has a larger mass and a larger radius but spins at the same initial angular velocity, the magnitude of the work required to stop it would be
a) Greater than W0
b) Equal to W0
c) Less than W0
d) There isn't enough information to know.
8) If we replace the original grindstone with one that has a larger mass and a smaller radius and which spins at the same initial angular velocity, the magnitude of the work required to stop it would be
a) Greater than W0
b) Equal to W0
c) Less than W0
d) There isn't enough information to know.