BackOn a level billiards table a cue ball, initially at rest at point O on the table, is struck so that it leaves the cue stick with a center-of-mass speed v₀ and ω₀ a “reverse” spin of angular speed (see Fig. 11–41). A kinetic friction force acts on the ball as it initially skids across the table. If ω₀ is 10% smaller than ωC , i.e., ω₀ = 0.90ωC, determine the ball’s cm velocity vCM when it starts to roll without slipping.
A 70.0-kg person stands on a tiny rotating platform with arms outstretched. One rotation takes 1.2 s when the person’s arms are outstretched. Ignore the moment of inertia of the lightweight platform. Determine the change in kinetic energy when the arms are lifted from the sides to the horizontal position.
A woman of mass m stands at the edge of a solid cylindrical platform of mass M and radius R. At t = 0, the platform is rotating with negligible friction at angular velocity ω0 about a vertical axis through its center, and the woman begins walking with speed υ (relative to the platform) toward the center of the platform. What will be the angular velocity when the woman reaches the center?
A 70.0-kg person stands on a tiny rotating platform with arms outstretched. From your answer to part (d), would you expect it to be harder or easier to lift your arms when rotating or when at rest?
A uniform disk turns at 4.1 rev/s around a frictionless central axis. A nonrotating rod, of the same mass as the disk and length equal to the disk’s diameter, is dropped onto the freely spinning disk, Fig. 11–32. They then turn together around the spindle with their centers superposed. What is the angular frequency in rev/s of the combination?
Suppose a star the size of our Sun, but with mass 8.0 times as great, were rotating at a speed of 1.0 revolution every 9.0 days. If it were to undergo gravitational collapse to a neutron star of radius 12 km, losing 0.70 of its mass in the process, what would its rotation speed be? Assume the star is a uniform sphere at all times. Assume also that the thrown-off mass carries off either its proportional share (0.70) of the initial angular momentum.
A 70.0-kg person stands on a tiny rotating platform with arms outstretched. If one rotation takes 1.2 s when the person’s arms are outstretched, what is the time for each rotation with arms at the sides? Ignore the moment of inertia of the lightweight platform.
A 4.2-m-diameter merry-go-round is rotating freely with an angular velocity of 0.80 rad/s. Its total moment of inertia is 1630 kg·m2. Four people standing on the ground, each of mass 65 kg, suddenly step onto the edge of the merry-go-round. What if the people were on it initially and then jumped off in a radial direction (relative to the merry-go-round)?
A person of mass 75 kg stands at the center of a rotating merry-go-round platform of radius 3.0 m and moment of inertia 920. kg·m². The platform rotates without friction with angular velocity 0.95 rad/s. The person walks radially to the edge of the platform. Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.
A thin uniform rod has a length of 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 and a moment of inertia about the axis of . 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 . The bug can be treated as a point mass. What is the mass of the rod.
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 if she pulls her arms in toward her body?
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 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 (comparable to our sun); its final radius is 16 km. If the original star rotated once in days, find the angular speed of the neutron star.
A certain gyroscope precesses at a rate of 0.50 rad/s when used on earth. If it were taken to a lunar base, where the acceleration due to gravity is 0.165g, what would be its precession rate?
Suppose a star the size of our Sun, but with mass 8.0 times as great, were rotating at a speed of 1.0 revolution every 9.0 days. If it were to undergo gravitational collapse to a neutron star of radius 12 km, losing 0.70 of its mass in the process, what would its rotation speed be? Assume the star is a uniform sphere at all times. Assume also that the thrown-off mass carries off either no angular momentum.
Suppose a 65-kg person stands at the edge of a 9.8-m-diameter merry-go-round turntable that is mounted on frictionless bearings and has a moment of inertia of 1850 kg·m2. The turntable is at rest initially, but when the person begins running at a speed of 3.8 m/s (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.