Problem 65
A carousel at the local carnival rotates once every \(45 \mathrm{~s}\). (a) What is the linear speed of an outer horse on the carousel, which is \(2.75 \mathrm{~m}\) from the axis of rotation? (b) What is the linear speed of an inner horse that is \(1.75 \mathrm{~m}\) from the axis of rotation?
Problem 66
The Crab Nebula One of the most studied objects in the night sky is the Crab Nebula. It is the remains of a supernova explosion observed by the Chinese in 1054. In 1968 it was discovered that a pulsar-a rapidly rotating neutron star that emits a pulse of radio waves with each revolution-lies near the center of the Crab Nebula. The amount of time required for each rotation of this pulsar is \(33 \mathrm{~ms}\). What is the angular speed (in \(\mathrm{rad} / \mathrm{s}\) ) of the pulsar?
Problem 67
Think \& Calculate As Tony the fisherman reels in a "big one," he turns the spool on his fishing reel at the rate of \(3.0\) complete revolutions every second. See Figure 8.26. (a) If the radius of the reel is \(3.7 \mathrm{~cm}\), what is the linear speed of the fishing line as it is reeled in? (b) How would your answer to part (a) change if the radius of the reel were doubled?
Problem 68
Give a common, everyday example for each of the following: (a) an object that has zero rotational kinetic energy but nonzero translational (linear) kinetic energy, (b) an object that has zero translational (linear) kinetic energy but nonzero rotational kinetic energy, (c) an object that has nonzero rotational and translational kinetic energies.
Problem 69
At the grocery store you pick up a can of beef broth and a can of chunky beef stew. The cans are identical in diameter and weight. Rolling both of them down the aisle with the same initial speed, you notice that the can of chunky stew rolls much farther than the can of broth. Why?
Problem 70
The minute and hour hands of a clock have a common axis of rotation and equal masses. The minute hand is long, thin, and uniform; the hour hand is short, thick, and uniform. (a) Is the moment of inertia of the minute hand greater than, less than, or equal to the moment of inertia of the hour hand? (b) Choose the best explanation from among the following: A. The hands have equal masses, and hence equal moments of inertia. B. Having mass farther from the axis of rotation results in a greater moment of inertia. C. The more compact hour hand has its mass more concentrated and thus has the greater moment of inertia.
Problem 71
A child pedals a tricycle, giving the large wheel an angular speed of \(0.373 \mathrm{rev} / \mathrm{s}\), as shown in Figure \(8.27 .\) If the radius of the wheel is \(0.260 \mathrm{~m}\), what is the child's linear speed?
Problem 72
An electric fan spinning with an angular speed of \(13 \mathrm{rad} / \mathrm{s}\) has a kinetic energy of \(4.6 \mathrm{~J}\). What is the moment of inertia of the fan?
Problem 73
A rotating disk has a mass of \(0.51 \mathrm{~kg}\), a radius of \(0.22 \mathrm{~m}\), and an angular speed of \(0.40 \mathrm{rad} / \mathrm{s}\). What is the angular momentum of the disk?
Problem 74
As a car travels down a road, the linear speed at the tops of its wheels is \(43 \mathrm{~m} / \mathrm{s}\). What is the linear speed of (a) the axles and (b) the bottoms of the wheels?
