Chapter 11: Q12Q (page 458)
What features of the Bohr model of hydrogen are consistent with the later, full quantum mechanical analysis? What features of the Bohr model had to be abandoned?
The features of the Bohr model are electrons revolve around the nucleus in stable orbits without emission of radiant energy.
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A sick of length and mass hangs from a low-friction axle (Figure 11.90). A bullet of mass travelling at a high speedstrikes near the bottom of the stick and quickly buries itself in the stick.
(a) During the brief impact, is the linear momentum of the stick + bullet system constant? Explain why or why not. Include in your explanation a sketch of how the stick shifts on the axle during the impact. (b) During the brief impact, around what point does the angular momentum of the stick + bullet system remain constant? (c) Just after the impact, what is the angular speed of the stick (with the bullet embedded in it) ? (Note that the center of mass of the stick has a speed The moment of inertia of a uniform rod about its center of mass is(d) Calculate the change in kinetic energy from just before to just after the impact. Where has this energy gone? (e) The stick (with the bullet embedded in it) swings through a maximum angleafter the impact, then swing back. Calculate .
An ice skater whirls with her arms and one leg stuck out as shown on the left in Figure 11.93, making one complete turn inThen she quickly moves her arms up above her head and pulls her leg in as shown at the right in Figure 11.93.
(a) Estimate how long it now takes for her to make one complete turn. Explain your calculations, and state clearly what approximations and estimates you make. (b) Estimate the minimum amount of chemical energy she must expended to change her configuration.
Give examples of translational angular momentum and rotational angular momentum in our Solar System.
Two gyroscopes are made exactly alike except that the spinning disk in one is made of low-density aluminum, whereas the disk in the other is made of high-density lead. If they have the same spin angular speeds and the same torque is applied to both, which gyroscope processes faster?
To complete this reflection, determine the relationship between and for the case of pure precession, but with the spin axis at an arbitrary angle to the vertical (figure) is the case of horizontal precession we treated). If you have the opportunity, see whether this relationship holds for a real gyroscope.
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