An elementary treatment of the theory of spinning tops and gyroscopic motion, by Harold Crabtree.

ANSWERS TO QUESTIONS.
CHAPTER I.
[1.] (a) [M][L2. (3) [M][L][T]-. (y) [M][L]2[T]-.
[2.] 448 lb.-ft.2. [3.] It is involved in the mass M. [4.] 40r.
[5.] Pt=M(v,-v). [6.] K. E=Wv2. [7.] Ps= M(vl2-v2).
CHAPTER II.
[8.] (i) It upsets it.
(ii) It causes it to precess.
[9.] (i) The further end dips.
(ii) The further end turns to the left.
(iii) The near end dips further.
[10.] (a) The front of the car is depressed.
(b) The back of the car is depressed.
[11.] (a) The bows turn to starboard.
(b) She heels to port.
[12.] The "Centrifugal Force."
CHAPTER III.
[13.] There is a small frictional couple at the toe, due to the toe not
being a mathematical point.
[14.] Because if the top begins to lean over, the gravity-couple about the
edge of support causes it to precess; and if the precession is
hindered by a rouygh surface, the top falls down.
[15.] There is more friction to "hurry" the precession.
[16.] The radius a is greater and thus o is reduced at a greater rate.
[17.] The final direction of friction is opposite to its initial direction.
[18.] In both cases the result of the air is the same. But if the peg is
blunt the effect of friction mentioned in question 13 is more
marked than in the case of the fine peg. On the other hand,
friction acts at a larger arm in the case of the blunt peg, so that a
smaller frictional force is capable of restoring o to the value
necessary for steady motion.
[19.] It would move in a vertical straight line; or if the motion were
steady it would be at rest.