V
if
Fig. 1.69.
Fig. 1.71.
1.265. A small body A is fixed to the inside of a thin rigid hoop of
radius R and mass equal to that of the body A. The hoop rolls without
slipping over a horizontal plane; at the moments when the body A
gets into the lower position, the centre of the hoop moves with velocity
vo (Fig. 1.68). At what values of vo will the hoop move without bouncing?
1.266. Determine the kinetic energy of a tractor crawler belt of
mass m if the tractor moves with velocity v (Fig. 1.69).
1.267. A uniform sphere of mass In and radius r rolls without sliding over a horizontal plane, rotating about a horizontal axle OA
(Fig. 1.70). In the process, the centre of the
sphere moves with velocity v along a circle
of radius R. Find the kinetic energy of the
sphere.
1.268. Demonstrate that in the reference
frame rotating with a constant angular
velocity o about a stationary axis a body
of mass m experiences the resultant
(a) centrifugal force of inertia Fit =
= mw2Rc, where Rc is the radius vector
of the body's centre of inertia relative to
the rotation axis;
(b) Coriolis force F ec„. = 2m [Irto], where
is the velocity of the body's centre of
inertia in the rotating reference frame.
1.269. A midpoint of a thin uniform rod AB of mass m and length
1 is rigidly fixed to a rotation axle 00' as shown in Fig. 1.71. The
rod is set into rotation with a constant angular velocity w. Find the
resultant moment of the centrifugal forces of inertia relative to the
point C in the reference frame fixed to the axle 00' and to the rod.
1.270. A conical pendulum, a thin uniform rod of length 1 and
mass nt, rotates uniformly about a vertical axis with angular velocity
oi (the upper end of the rod is hinged). Find the angle 0 between the
rod and the vertical.
1.271. A uniform cube with edge a rests on a horizontal plane whose
friction coefficient equals k. The cube is set in motion with an initial
velocity, travels some distance over the plane and comes to a stand54
if
Fig. 1.69.
Fig. 1.71.
1.265. A small body A is fixed to the inside of a thin rigid hoop of
radius R and mass equal to that of the body A. The hoop rolls without
slipping over a horizontal plane; at the moments when the body A
gets into the lower position, the centre of the hoop moves with velocity
vo (Fig. 1.68). At what values of vo will the hoop move without bouncing?
1.266. Determine the kinetic energy of a tractor crawler belt of
mass m if the tractor moves with velocity v (Fig. 1.69).
1.267. A uniform sphere of mass In and radius r rolls without sliding over a horizontal plane, rotating about a horizontal axle OA
(Fig. 1.70). In the process, the centre of the
sphere moves with velocity v along a circle
of radius R. Find the kinetic energy of the
sphere.
1.268. Demonstrate that in the reference
frame rotating with a constant angular
velocity o about a stationary axis a body
of mass m experiences the resultant
(a) centrifugal force of inertia Fit =
= mw2Rc, where Rc is the radius vector
of the body's centre of inertia relative to
the rotation axis;
(b) Coriolis force F ec„. = 2m [Irto], where
is the velocity of the body's centre of
inertia in the rotating reference frame.
1.269. A midpoint of a thin uniform rod AB of mass m and length
1 is rigidly fixed to a rotation axle 00' as shown in Fig. 1.71. The
rod is set into rotation with a constant angular velocity w. Find the
resultant moment of the centrifugal forces of inertia relative to the
point C in the reference frame fixed to the axle 00' and to the rod.
1.270. A conical pendulum, a thin uniform rod of length 1 and
mass nt, rotates uniformly about a vertical axis with angular velocity
oi (the upper end of the rod is hinged). Find the angle 0 between the
rod and the vertical.
1.271. A uniform cube with edge a rests on a horizontal plane whose
friction coefficient equals k. The cube is set in motion with an initial
velocity, travels some distance over the plane and comes to a stand54