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

16

ROTATION ABOUT A FIXED AXIS

similar considerations; but the student may feel at first that
he is dealing with a different kind of velocity, and a different
(i.e. angular) measurement of space. In order, therefore, to
obtain a clearer realisation of the quantities employed, the
dimensions of the equations should be considered, this being
a most important method of checking algebraical expressions.
Dimensions. (1) 2 = w+ at;
[T] [T] + ]2x [L '
[T]-1 = [T2]-1 + [T]-1.
(2) 0=t + at2;
[T] [T]2'
(3) = + 2a0;
[T]- = [T]-2 + [TI-2.
EXAMPLES.
1. A wheel acquires a velocity of 100 rad./sec. in 16 sees. under a uniform
angular acceleration, having started from rest. Find the acceleration.
2. Through what angle has it revolved in the 16 sees.? What angle will
it turn through in the next 16 sees.?
3. A wheel is given an initial velocity of 1,000 revolutions per sec., after
which it is acted on by a uniform retardation which in 3 sees. reduces
its velocity by 12 revolutions a second. How many revolutions will it have
made from the start when it is making 20 revolutions a second?
8. Inertia. Newton's First Law of Motion asserts that,
Every body will continue in its state of rest or of uniform
motion in a straight line, except in so far as it is compelled by
impressed forces to change that state; which is equivalent to
saying that a body has no power of itself to change its state
of rest or of uniform motion in a straight line. This statement is sometimes called the "Law of Inertia," " inertia" being
regarded as a property of mass (Latin: iners).
Newton's Third Law of Motion asserts that, To every action
there is an equal and opposite reaction; and thus the existence
of a force implies of necessity some resistance against which the
force is applied. When a force is applied to a body at rest the
resistance offered by the body is due to the inertia of its mass.
If the body had no mass no force could be exerted on it. So
also, if we attempt to alter the existing motion of a body, a
resistance is experienced. This co-existence of action and reaction
is described by the term stress; and the resistance which a body
offers by reason of its mass is sometimes called the force of
inertia of the body, meaning the resistance due to inertia.