110
3 Rotational Kinematics
Fig. 3.3
3.17 A wire bent in the form ABC passes through a ring B as in Fig. 3.4. The ring
rotates with constant speed in a horizontal circle of radius r . Show that the
speed of rotation is
√ gr if the wires are to maintain the form.
Fig. 3.4
A
C
B
60 °
30 °
r
3.18 A small cube placed on the inside of a funnel rotates about a vertical axis at
a constant rate of f rev/s. The wall of the funnel makes an angle θ with the
horizontal (Fig. 3.5). If the coefficient of static friction is μ and the centre
of the cube is at a distance r from the axis of rotation, show that the largest
frequency for which the block will not move with respect to the funnel is
f max =
1
2π
g(sin θ + μ cos θ)
r (cos θ − μ sin θ)
Fig. 3.5
3 Rotational Kinematics
Fig. 3.3
3.17 A wire bent in the form ABC passes through a ring B as in Fig. 3.4. The ring
rotates with constant speed in a horizontal circle of radius r . Show that the
speed of rotation is
√ gr if the wires are to maintain the form.
Fig. 3.4
A
C
B
60 °
30 °
r
3.18 A small cube placed on the inside of a funnel rotates about a vertical axis at
a constant rate of f rev/s. The wall of the funnel makes an angle θ with the
horizontal (Fig. 3.5). If the coefficient of static friction is μ and the centre
of the cube is at a distance r from the axis of rotation, show that the largest
frequency for which the block will not move with respect to the funnel is
f max =
1
2π
g(sin θ + μ cos θ)
r (cos θ − μ sin θ)
Fig. 3.5