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Chapter 9: Q18P (page 378)
If an object鈥檚 rotational kinetic energy is 50 J and it rotates with an angular speed of 12 rad/s, what is the moment of inertia?
The moment of inertia is, .
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Discuss qualitatively the motion of the atoms in a block of steel that falls onto another steel block. Why and how do large-scale vibrations damp out?
By calculating numerical quantities for a multiparticle system. One can get a concrete sense of the meaning of the relationships and . Consider an object consisting of two balls connected by a spring, whose stiffness is 400 N/m. The object has been thrown through the air and is rotating and vibrating as it moves. At a particular instant, the spring is stretched 0.3m, and the two balls at the ends of the spring have the following masses and velocities:
(a)For this system, calculate . (b) Calculate (c) Calculate 3. (d) Calculate . (e) Calculate . (f) Here is a way to check your result for . The velocity of a particle relative to the center of mass is calculated by subtracting from the particle鈥檚 velocity. To take a simple example, if you鈥檙e riding in a car that鈥檚 moving with and you throw a ball with , relative to the car, a bystander on the ground sees the ball moving with So and therefore we havefor each mass and calculate the corresponding. Compare with the result you obtained in part (e).
A man whose mass is and a woman whose mass is sit at opposite ends of a canoe long, whose mass is . (a) Relative to the man, where is the mass of the system consisting of man-woman, and canoe? (Hint: Choose a specific coordinate system with a specific origin.) (b) Suppose that the man moves quickly to the center of the canoe and sits down there. How far does the canoe move in the water? Explain your work and your assumptions.
A string is wrapped around a disk of mass 2.1 kg (its density is not necessarily uniform). Starting from rest, you pull the string with a constant force of 9 N along a nearly frictionless surface. At the instant when the center of the disk has moved a distance 0.11 m, your hand has moved a distance of 0.28 m (Figure 9.51).
(a) At this instant, what is the speed of the center of mass of the disk? (b) At this instant, how much rotational kinetic energy does the disk have relative to its center of mass? (c) At this instant, the angular speed of the disk is 75 rad/s. What is the moment of inertia of the disk?
Three uniform-density spheres are positioned as follows:
What is the location of the center of mass of this three-sphere system?
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