of the vector of the ball's angular momentum relative to the point
0 picked up during half a revolution.
1.189. A ball of mass m falls down without initial velocity from
a height h over the Earth's surface. Find the increment of the ball's
angular momentum vector picked up during the time of falling (rela-tive to the point (^0) of the reference frame moving translationally in
a horizontal direction with a velocity 1 7 ). The ball starts falling
from the point 0. The air drag is to be neglected.
1.190. A smooth horizontal disc rotates with a constant angular
velocity co about a stationary vertical axis passing through its centre,
the point 0. At a moment t = 0 a disc is set in motion from that
177 Vg
Im/2
m/2
Fig. 1.49. Fig. 1.50.
point with velocity vo. Find the angular momentum M (t) of the
disc relative to the point 0 in the reference frame fixed to the disc.
Make sure that this angular momentum is caused by the Coriolis
force.
1.191. A particle moves along a closed trajectory in a central
field of force where the particle's potential energy U = kr 2 (k is a
positive constant, r is the distance of the particle from the centre 0
of the field). Find the mass of the particle if its minimum distance
from the point 0 equals r 1 and its velocity at the point farthest from 0
equals v 2.
1.192. A small ball is suspended from a point 0 by a light thread
of length 1. Then the ball is drawn aside so that the thread deviates
through an angle 0 from the vertical and set in motion in a hori-
zontal direction at right angles to the vertical plane in which the
thread is located. What is the initial velocity that has to be imparted
to the ball so that it could deviate through the maximum angle at/2
in the process of motion?
1.193. A small body of mass m tied to a non-stretchable thread
moves over a smooth horizontal plane. The other end of the thread
is being drawn into a hole 0 (Fig. 1.49) with a constant velocity.
Find the thread tension as a function of the distance r between the
body and the hole if at r = ro the angular velocity of the thread is
equal to coo.
1.194. A light non-stretchable thread is wound on a massive fixed
pulley of radius R. A small body of mass m is tied to the free end
of the thread. At a moment t = 0 the system is released and starts
moving. Find its angular momentum relative to the pulley axle as
a function of time t.
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