(II) Two ice skaters, both of mass 68 kg, approach on parallel paths 1.6 m apart. Both are moving at 3.5 m/s with their arms outstretched. They join hands as they pass, still maintaining their 1.6-m separation, and begin rotating about one another. Treat the skaters as particles with regard to their rotational inertia.
(c) If they now pull on each other’s hands, reducing their radius to half its original value, what is their common angular speed after reducing their radius?

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

(a) no angular momentum.

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

(b) its proportional share (0.70) of the initial angular momentum.

A 70.0-kg person stands on a tiny rotating platform with arms outstretched.

(c) 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 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.

(d) Determine the change in kinetic energy when the arms are lifted from the sides to the horizontal position.

A 70.0-kg person stands on a tiny rotating platform with arms outstretched.

(e) 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?

(III) On 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.

(b) Using conservation of angular momentum, find the critical angular speed ω_C such that, if ω₀=ω_C, kinetic friction will bring the ball to a complete (as opposed to momentary) stop. <IMAGE>

(III) On 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.

(c) If ω₀ is 10% smaller than ω_C , i.e., ω₀ = 0.90ω_C , determine the ball’s cm velocity v_CM when it starts to roll without slipping.

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(III) On 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.

(d) If ω₀ is 10% larger than ,w_C i.e.,ω₀ = 1.10w_C, determine the ball’s cm velocity v_CM when it starts to roll without slipping. [Hint: The ball possesses two types of angular momentum, the first due to the linear speed v_CM of its cm relative to point O, the second due to the spin at angular velocity ω about its own cm. The ball’s total L about O is the sum of these two angular momenta.]

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