Chapter 8: 8-15Q (page 198)
Can the diver of Fig. 8–28 do a somersault without having any initial rotation when she leaves the board? Explain.
Yes, the diver can perform a somersault without having any initial rotation when she leaves the board.
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(II) A bowling ball of mass 7.25 kg and radius 10.8 cm rolls without slipping down a lane at\({\bf{3}}{\bf{.10 m/s}}\).Calculate its total kinetic energy.
A wheel of mass M has radius R. It is standing vertically on the floor, and we want to exert a horizontal force F at its axle so that it will climb a step against which it rests (Fig. 8–60). The step has height h, where h < R. What minimum force F is needed?
Determine the angular momentum of the Earth (a) about its rotation axis (assume the Earth is a uniform sphere), and (b) in its orbit around the Sun (treat the Earth as a particle orbiting the Sun).
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 that is possessed by planets using a simplified model which includes only the large outer planets with the most angular momentum. The central Sun (mass\(1.99 \times {10^{30}}\;{\rm{kg}}\), radius\(6.96 \times {10^8}\;{\rm{m}}\)) 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.
Planet | Mean Distance from Sun\(\left( { \times {{10}^6}\;{\rm{km}}} \right)\) | Orbital Period (Earth Years) | Mass \(\left( { \times {{10}^{25}}\;{\rm{kg}}} \right)\) |
Jupiter | 778 | 11.9 | 190 |
Saturn | 1427 | 29.5 | 56.8 |
Uranus | 2870 | 84.0 | 8.68 |
Neptune | 4500 | 165 | 10.2 |
A small mass m on a string is rotating without friction in a circle. The string is shortened by pulling it through the axis of rotation without any external torque, Fig. 8–39. What happens to the tangential velocity of the object?
(a) It increases.
(b) It decreases.
(c) It remains the same.
FIGURE 8-39
MisConceptual Questions 10 and 11.
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