11.4 Precession of a Gyroscope

A top has a precession frequency of 5.0 rad/s on Earth. What is its precession frequency on the Moon?

Gyroscopes used in guidance systems to indicate directions in space must have an angular momentum that does not change in direction. When placed in the vehicle, they are put in a compartment that is separated from the main fuselage, such that changes in the orientation of the fuselage does not affect the orientation of the gyroscope. If the space vehicle is subjected to large forces and accelerati…

A gyroscope has a 0.5-kg disk that spins at 40 rev/s. The center of mass of the disk is 15 cm from a pivot with a radius of the disk of 10 cm. What is the precession angular velocity?

Repeat the preceding problem replacing the marble with a hollow sphere. Explain the new results.

Repeat the preceding problem for a hollow sphere of the same radius and mass and initial speed. Explain the differences in the results.

A 4.0-kg particle moves in a circle of radius 2.0 m. The angular momentum of the particle varies in time according to $l = 5.0 t^{2} .$ (a) What is the torque on the particle about the center of the circle at $t = 3.4 \text{s}$? (b) What is the angular velocity of the particle at $t = 3.4 \text{s}$?

(a) What is the angular momentum of the Moon in its orbit around Earth? (b) How does this angular momentum compare with the angular momentum of the Moon on its axis? Remember that the Moon keeps one side toward Earth at all times.

A potter’s disk spins from rest up to 10 rev/s in 15 s. The disk has a mass 3.0 kg and radius 30.0 cm. What is the angular momentum of the disk at $t = 5 \text{s}, t = 1 \text{0 s}$?

A solid cylinder of mass 2.0 kg and radius 20 cm is rotating counterclockwise around a vertical axis through its center at 600 rev/min. A second solid cylinder of the same mass and radius is rotating clockwise around the same vertical axis at 900 rev/min. If the cylinders couple so that they rotate about the same vertical axis, what is the angular velocity of the combination?

Eight children, each of mass 40 kg, climb on a small merry-go-round. They position themselves evenly on the outer edge and join hands. The merry-go-round has a radius of 4.0 m and a moment of inertia $1000.0 \text{kg} \cdot \text{m}^{2}$. After the merry-go-round is given an angular velocity of 6.0 rev/min, the children walk inward and stop when they are 0.75 m from the axis of rotation. What is the new angular velocity of the merry…

A satellite in the shape of a sphere of mass 20,000 kg and radius 5.0 m is spinning about an axis through its center of mass. It has a rotation rate of 8.0 rev/s. Two antennas deploy in the plane of rotation extending from the center of mass of the satellite. Each antenna can be approximated as a rod has mass 200.0 kg and length 7.0 m. What is the new rotation rate of the satellite?