16. Angular Momentum

Which statement best explains how both planets orbiting the Sun and figure skaters spinning on ice conserve angular momentum ($L$)?

According to the conservation of angular momentum, what happens to the rotational speed of a spinning star if its diameter $d$ increases while no external torque acts on it?

Under which condition is the angular momentum $L$ of a system constant?

Under what condition is the angular momentum $L$ of an object conserved?

Based on the conservation of angular momentum ($L=I\mathrm{C9}$), what happens to the angular velocity ($\mathrm{C9}$) of a figure skater when they pull their arms in during a spin, assuming no external torques act on the system?

Based on the conservation of $\mathrm{angular} \mathrm{momentum}$, how does one expect the planets to spin as they form from a rotating cloud of gas and dust?

According to the conservation of angular momentum ($L$), what happens when a spinning ice skater draws in her outstretched arms?

According to the law of conservation of angular momentum, the angular momentum $L$ of a system remains constant if which of the following conditions is satisfied?

In the context of conservation of angular momentum, consider the system shown in Figure 2, part e. For which of the following diagrams is the $L$ (angular momentum) of the system constant?

An ice skater is spinning with her arms out and is not being acted upon by an external torque. What happens to her angular velocity $\omega$ if she pulls her arms in toward her body?

Suppose a diver spins at 8 rad/s while falling with a moment of inertia about an axis through himself of 3 kg•m². What moment of inertia would the diver need to have to spin at 4 rad/s? 

BONUS:How could he accomplish this?

Two astronauts, both 80 kg, are connected in space by a light cable. When they are 10 m apart, they spin about their center of mass with 6 rad/s. Calculate the new angular speed they'll have if they pull on the rope to reduce their distance to 5 m. You may treat them as point masses, and assume they continue to spin around their center of mass.

The rotor (flywheel) of a toy gyroscope has mass 0.140 kg. Its moment of inertia about its axis is 1.20 × 10^-4 kg m². The mass of the frame is 0.0250 kg. The gyroscope is supported on a single pivot (Fig. E10.51) with its center of mass a horizontal distance of 4.00 cm from the pivot. The gyroscope is precessing in a horizontal plane at the rate of one revolution in 2.20 s. Find the upward force exerted by the pivot.

<Image>

Under some circumstances, a star can collapse into an extremely dense object made mostly of neutrons and called a neutron star. The density of a neutron star is roughly ${10}^{14}$ times as great as that of ordinary solid matter. Suppose we represent the star as a uniform, solid, rigid sphere, both before and after the collapse. The star's initial radius was $7.0\times {10}^5\text{ km}$ (comparable to our sun); its final radius is 16 km. If the original star rotated once in $30$ days, find the angular speed of the neutron star.

A thin uniform rod has a length of $0.500\text{ m}$ and is rotating in a circle on a frictionless table. The axis of rotation is perpendicular to the length of the rod at one end and is stationary. The rod has an angular velocity of $0.400\text{ rad/s}$ and a moment of inertia about the axis of $3.00\times {10}^{-3}{\text{kg/m}}^2$. A bug initially standing on the rod at the axis of rotation decides to crawl out to the other end of the rod. When the bug has reached the end of the rod and sits there, its tangential speed is $0.160\text{ m/s}$. The bug can be treated as a point mass. What is the mass of the rod.