tain moment the man starts moving along the edge of the disc; he
shifts over an angle cp' relative to the disc and then stops. In the process of motion the velocity of the man varies with time as v' (t).
Assuming the dimensions of the man to be negligible, find:
(a) the angle through which the disc had turned by the moment the
man stopped;
(b) the force moment (relative to the rotation axis) with which
the man acted on the disc in the process of motion.
1.278. Two horizontal discs rotate freely about a vertical axis passing through their centres. The moments of inertia of the discs relative
to this axis are equal to /1 and /2, and the angular velocities to oh
and co,. When the upper disc fell on the lower one, both discs began
rotating, after some time, as a single whole (due to friction). Find:
(a) the steady-state angular rotation velocity of the discs;
(b) the work performed by the friction forces in this process.
1.279. A small disc and a thin uniform rod of length 1, whose mass
is i times greater than the mass of the disc, lie on a smooth horizontal plane. The disc is set in motion, in horizontal direction and perpendicular to the rod, with velocity v, after which it elastically
collides with the end of the rod. Find
the velocity of the disc and the angular velocity of the rod after the collision. At what value of ii will the
velocity of the disc after the collision be equal to zero? reverse its direction?
1.280. A stationary platform P
which can rotate freely about a vertical axis (Fig. 1.72) supports a motor M
and a balance weight N. The mo0
ment of inertia of the platform
with the motor and the balance weight
Fig. 1.72.
relative to this axis is equal to I. A
light frame is fixed to the motor's shaft with a uniform sphere A rotating freely with an angular velocity o about a shaft BB' coinciding with the axis 00'. The moment of inertia of the sphere relative
to the rotation axis is equal to I. Find:
(a) the work performed by the motor in turning the shaft BB'
through 90'; through 180°;
(b) the moment of external forces which maintains the axis of the
arrangement in the vertical position after the motor turns the shaft
BB' through 90°.
1.281. A horizontally oriented uniform rod AB of mass m =
= 1.40 kg and length 1, = 100 cm rotates freely about a stationary
vertical axis 00' passing through its end A. The point A is located
at the middle of the axis 00' whose length is equal to 1= 55 cm.
At what angular velocity of the rod the horizontal component of the
force acting on the lower end of the axis 00' is equal to zero? What
56
shifts over an angle cp' relative to the disc and then stops. In the process of motion the velocity of the man varies with time as v' (t).
Assuming the dimensions of the man to be negligible, find:
(a) the angle through which the disc had turned by the moment the
man stopped;
(b) the force moment (relative to the rotation axis) with which
the man acted on the disc in the process of motion.
1.278. Two horizontal discs rotate freely about a vertical axis passing through their centres. The moments of inertia of the discs relative
to this axis are equal to /1 and /2, and the angular velocities to oh
and co,. When the upper disc fell on the lower one, both discs began
rotating, after some time, as a single whole (due to friction). Find:
(a) the steady-state angular rotation velocity of the discs;
(b) the work performed by the friction forces in this process.
1.279. A small disc and a thin uniform rod of length 1, whose mass
is i times greater than the mass of the disc, lie on a smooth horizontal plane. The disc is set in motion, in horizontal direction and perpendicular to the rod, with velocity v, after which it elastically
collides with the end of the rod. Find
the velocity of the disc and the angular velocity of the rod after the collision. At what value of ii will the
velocity of the disc after the collision be equal to zero? reverse its direction?
1.280. A stationary platform P
which can rotate freely about a vertical axis (Fig. 1.72) supports a motor M
and a balance weight N. The mo0
ment of inertia of the platform
with the motor and the balance weight
Fig. 1.72.
relative to this axis is equal to I. A
light frame is fixed to the motor's shaft with a uniform sphere A rotating freely with an angular velocity o about a shaft BB' coinciding with the axis 00'. The moment of inertia of the sphere relative
to the rotation axis is equal to I. Find:
(a) the work performed by the motor in turning the shaft BB'
through 90'; through 180°;
(b) the moment of external forces which maintains the axis of the
arrangement in the vertical position after the motor turns the shaft
BB' through 90°.
1.281. A horizontally oriented uniform rod AB of mass m =
= 1.40 kg and length 1, = 100 cm rotates freely about a stationary
vertical axis 00' passing through its end A. The point A is located
at the middle of the axis 00' whose length is equal to 1= 55 cm.
At what angular velocity of the rod the horizontal component of the
force acting on the lower end of the axis 00' is equal to zero? What
56