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- Saturns ring system forms a relatively thin, circular disk in the equatorial plane of the planet. The inner radius of the ring system is approximately 92,000 km from the center of the planet, and the outer edge is about 137,000 km from the center of the planet. The mass of Saturn itself is 5.68 1026 kg. a. What is the period of a particle in the outer edge compared with the period of a particle in the inner edge? b. How long does it take a particle in the inner edge to move once around Saturn? c. While this inner-edge particle is completing one orbit abound Saturn, how far around Saturn does a particle on the outer edge move?A Two particles A and B move at a constant speed in circular paths at the same angular speed . Particle As circle has a radius that is twice the length of particle Bs circle. What is the ratio TA/TB of their periods?A pendulum consists of a small object called a bob hanging from a light cord of fixed length, with the top end of the cord fixed, as represented in Figure CQ7.5. The bob moves without friction, swinging equally high on both sides. It moves from its turning point A through point B and reaches its maximum speed at point C. (a) At what point does the bob have non-zero radial acceleration and zero tangential acceleration? What is the direction of its total acceleration at this point? (b) At what point does the bob have nonzero tangential acceleration and zero radial acceleration? What is the direction of its total acceleration at this point? (c) At what point does the bob have both nonzero tangential and radial acceleration? What is the direction of its total acceleration at this point? Figure CQ7.5
- Studies of the relationship of the Sun to our galaxythe Milky Wayhave revealed that the Sun is located near the outer edge of the galactic disc, about 30 000 ly (1 ly = 9.46 1015 m) from the center. The Sun has an orbital speed of approximately 250 km/s around the galactic center. (a) What is the period of the Suns galactic motion? (b) What is the order of magnitude of the mass of the Milky Way galaxy? (c) Suppose the galaxy is made mostly of stars of which the Sun is typical. What is the order of magnitude of the number of stars in the Milky Way?Unreasonable Results (a) Based on Kepler's laws and information on the orbital characteristics of the Moon, calculate the orbital radius for an Earth satellite having a period of 1.00 h. (b) What is unreasonable about this result? (c) What is unreasonable or inconsistent about the premise of a 1.00 h orbit?(a) Given that the period of the Moons orbit about the Earth is 27.32 days and the nearly constant distance between the center of the Earth and the center of the Moon is 3.84 108 m, use Equation 13.11 to calculate the mass of the Earth. (b) Why is the value you calculate a bit too large?
- (a) Calculate the magnitude of the acceleration due to gravity on the surface of Earth due to the Moon. (b) Calculate the magnitude of the acceleration due to gravity at Earth due to the Sun. (c) Take the ratio of the Moon's acceleration to the Sun's and comment on why the tides are predominantly due to the Moon in spite of this number.Review. Assume a certain liquid, with density 1 230 kg/m3, exerts no friction force on spherical objects. A ball of mass 2.10 kg and radius 9.00 cm is dropped from rest into a deep tank of this liquid from a height of 3.30 m above the surface. (a) Find the speed at which the hall enters the liquid. (b) Evaluate the magnitudes of the two forces that are exerted on the ball as it moves through the liquid. (c) Explain why the ball moves down only a limited distance into the liquid and calculate this distance. (d) With what speed will the ball pop up out of the liquid? (c) How does the time interval tdown, during which the ball moves from the surface down to its lowest point, compare with the lime interval tup for the return trip between the same two points? (f) What If? Now modify the model to suppose the liquid exerts a small friction force on the ball, opposite in direction to its motion. In this case, how do the time intervals tdown and tup compare? Explain your answer with a conceptual argument rather than a numerical calculation.Astronomical observatrions of our Milky Way galaxy indicate that it has a mass of about 8.01011 solar masses. A star orbiting on the galaxy’s periphery is about 6.0104 light-years from its center. (a) What should the orbital period of that star be? (b) If its period is 6.0107 years instead, what is the mass of the galaxy? Such calculations are used to imply the existence of other matter, such as a very massive black hole at the center of the Milky Way.
- The motion of spinning a hula hoop around one's hips can bemodeled as a hoop rotating around an axis not through the center, but offset from the center by an amount h, where h is lessthan R, the radius of the hoop. Suppose Maria spins a hula hoopwith a mass of 0.75 kg and a radius of 0.62 m around her waist.The rotation axis is perpendicular to the plane of the hoop, butapproximately 0.40 m from the center of the hoop. a. What isthe rotational inertia of the hoop in this case? b. If the hula hoopis rotating with an angular speed of 13.7 rad/s, what is its rotational kinetic energy?In Example 2.6, we considered a simple model for a rocket launched from the surface of the Earth. A better expression for the rockets position measured from the center of the Earth is given by y(t)=(R3/2+3g2Rt)2/3j where R is the radius of the Earth (6.38 106 m) and g is the constant acceleration of an object in free fall near the Earths surface (9.81 m/s2). a. Derive expressions for vy(t) and ay(t). b. Plot y(t), vy(t), and ay(t). (A spreadsheet program would be helpful.) c. When will the rocket be at y=4R? d. What are vy and ay when y=4R?A series of five 0.1-kg spheres are arrayed along a thin, lightweight rigid rod with length 0.5 m at intervals of 0,1m from one end of the rod. The system spins about an axis perpendicular to and passing through the unoccupied end of the rod with a period of 0.3 s. In this way, each mass moves in the same plane along a circular path whose radius is its distance from the rotation axis. (a) How far does each mass move during one revolution? (b) What is the speed of each mass as it orbits the axis? (c) What is the total angular momentum of the system?