3.2 Problems
109
Fig. 3.2 Conical pendulum
3.11 If the number of steady revolutions per minute of a conical pendulum is
increased from 70 to 80, what would be the difference in the level of the bob?
3.12 A central wheel can rotate about its central axis, which is vertical. From a
point on the rim hangs a simple pendulum. When the wheel is caused to rotate
uniformly, the angle of inclination of the pendulum to the vertical is θ 0 . If the
radius of the wheel is R cm and the length of the pendulum is 1 cm, obtain an
expression for the number of rotations of the wheel per second.
[University of Newcastle]
3.13 A coin is placed at a distance r from the centre of a gramophone record rotating with angular frequency ω = 2π f . Find the maximum frequency for which
the coin will not slip if μ is the coefficient of friction.
3.14 A particle of mass m is attached to a spring of initial length L 0 and spring
constant k and rotated in a horizontal plane with an angular velocity ω. What
is the new length of the spring and the tension in the spring?
3.15 A hollow cylinder drum of radius r is placed with its axis vertical. It is rotated
about an axis passing through its centre and perpendicular to the face and a
coin is placed on the inside surface of the drum. If the coefficient of friction is
μ, what is the frequency of rotation so that the coin does not fall down?
3.16 A bead B is threaded on a smooth circular wire frame of radius r , the radius
vector
r making an angle θ with the negative z-axis (see Fig. 3.3). If the frame
is rotated with angular velocity ω about the z-axis then show that the bead will
be in equilibrium if ω =
g
r cos θ
.
109
Fig. 3.2 Conical pendulum
3.11 If the number of steady revolutions per minute of a conical pendulum is
increased from 70 to 80, what would be the difference in the level of the bob?
3.12 A central wheel can rotate about its central axis, which is vertical. From a
point on the rim hangs a simple pendulum. When the wheel is caused to rotate
uniformly, the angle of inclination of the pendulum to the vertical is θ 0 . If the
radius of the wheel is R cm and the length of the pendulum is 1 cm, obtain an
expression for the number of rotations of the wheel per second.
[University of Newcastle]
3.13 A coin is placed at a distance r from the centre of a gramophone record rotating with angular frequency ω = 2π f . Find the maximum frequency for which
the coin will not slip if μ is the coefficient of friction.
3.14 A particle of mass m is attached to a spring of initial length L 0 and spring
constant k and rotated in a horizontal plane with an angular velocity ω. What
is the new length of the spring and the tension in the spring?
3.15 A hollow cylinder drum of radius r is placed with its axis vertical. It is rotated
about an axis passing through its centre and perpendicular to the face and a
coin is placed on the inside surface of the drum. If the coefficient of friction is
μ, what is the frequency of rotation so that the coin does not fall down?
3.16 A bead B is threaded on a smooth circular wire frame of radius r , the radius
vector
r making an angle θ with the negative z-axis (see Fig. 3.3). If the frame
is rotated with angular velocity ω about the z-axis then show that the bead will
be in equilibrium if ω =
g
r cos θ
.