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Chapter 8: 8-14Q (page 198)
We claim that momentum and angular momentum are conserved. Yet most moving or rotating objects eventually slow down and stop. Explain.
Due to the presence of the frictional force, the net force on the object is not equal to zero. That’s why most moving or rotating objects slow down and stop.
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If the coefficient of static friction between a car’s tires and the pavement is 0.65, calculate the minimum torque that must be applied to the 66-cm-diameter tire of a 1080-kg automobile in order to “lay rubber” (make the wheels spin, slipping as the car accelerates). Assume each wheel supports an equal share of the weight.
A 4.00-kg mass and a 3.00-kg mass are attached to opposite ends of a very light 42.0-cm-long horizontal rod (Fig. 8–61). The system is rotating at angular speed\(\omega = 5.60\;{\rm{rad/s}}\)about a vertical axle at the center of the rod. Determine (a) the kinetic energy KE of the system, and (b) the net force on each mass.
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 |
Can the diver of Fig. 8–28 do a somersault without having any initial rotation when she leaves the board? Explain.
(a) A grinding wheel 0.35 m in diameter rotates at 2200 rpm. Calculate its angular velocity in \({{{\bf{rad}}}\mathord{\left/{\vphantom{{{\bf{rad}}} {\bf{s}}}} \right.} {\bf{s}}}\).(b) What are the linear speed and acceleration of a point on the edge of the grinding wheel?
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