Fig. 1.54.
disc equals m = 7.3 kg. Find the moment of inertia of such a disc
relative to the axis passing through its centre of inertia and perpen-
dicular to the plane of the disc.
1.242. Using the formula for the moment of inertia of a uniform
sphere, find the moment of inertia of a thin spherical layer of
mass
m and radius
R
relative to the axis passing through its centre.
1.243. A light thread with a body of mass m tied to its end is wound
on a uniform solid cylinder of mass
M
and radius
R
(Fig. 1.55). At
a moment
t
= 0 the system is set in motion.
Assuming the friction in the axle of the cylin-
der to be negligible, find the time dependence
of
(a)
the angular velocity of the cylinder;
(b)
the kinetic energy of the whole system.
1.244. The ends of thin threads tightly
wound on the axle of radius
r
of the Maxwell
disc are attached to a horizontal bar. When
the disc unwinds, the bar is raised to keep the
disc at the same height. The mass bf the disc
with the axle is equal to m, the moment of
inertia of the arrangement relative to its axis is
I.
Find the tension of
each thread and the acceleration of the bar.
1.245. A thin horizontal uniform rod
AB
of mass m and length 1
can rotate freely about a vertical axis passing through its end
A.
At a certain moment the end
B
starts experiencing a constant force
Fig. 1.55.
Fig. 1.56.
F
which is always perpendicular to the original position of the sta-
tionary rod and directed in a horizontal plane. Find the angular ve-
locity of the rod as a function of its rotation angle op counted relative
to the initial position.
1.246. In the arrangement shown in Fig. 1.56 the mass of the uni-
form solid cylinder of radius
R
is equal to
m
and the masses of two
bodies are equal to m, and
m
2
.
The thread slipping and the friction
in the axle of the cylinder are supposed to be absent. Find the angular
acceleration of the cylinder and the ratio of tensions T
i
/T, of the
vertical sections of the thread in the process of motion.
4-9451
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