16. Angular Momentum

(II) A potter’s wheel is rotating around a vertical axis through its center at a frequency of 1.5 rev/s . The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 2.8-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after the clay sticks to it?

(II) A uniform stick 1.0 m long with a total mass of 270 g is pivoted at its center. A 3.5-g bullet is shot through the stick midway between the pivot and one end (Fig. 11–37). The bullet approaches at 250 m/s and leaves at 140 m/s. With what angular speed is the stick spinning after the collision?

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(II) Suppose a 5.2 x 10¹⁰kg meteorite struck the Earth at the equator with a speed v = 2.2 x 10⁴ m/s , as shown in Fig. 11–38 and remained stuck. By what factor would this affect the rotational frequency of the Earth (1 rev/day)?

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(III) A thin uniform rod of mass M and length ℓ rests on a frictionless table and is struck at a point ℓ/4 from its cm by a clay ball of mass m moving at speed υ (Fig. 11–40). The ball sticks to the rod. Determine the translational and rotational motion of the rod after the collision.

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Most of our Solar System’s mass is contained in the Sun, and the planets possess almost all of the Solar System’s angular momentum. This observation plays a key role in theories attempting to explain the formation of our Solar System. Estimate the fraction of the Solar System’s total angular momentum from the planets using a simplified model which includes only the large outer planets with the most angular momentum. The central Sun (mass 1.99 x 10³⁰ kg , radius 6.96 x 10⁸ m ) spins about its axis once every 25 days and the planets Jupiter, Saturn, Uranus, and Neptune move in nearly circular orbits around the Sun with orbital data given in the Table below. Ignore each planet’s spin about its own axis.

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