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Chapter 11: Q9Q (page 458)
Consider a rotating star far from other objects. Its rate of spin stays constant, and its axis of rotation keeps pointing in the same direction. Why?
The rate of spin stays constant, and its axis of rotation keeps pointing in the same direction due to the angular momentum.
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In Figure11.89depicts a device that can rotate freely with little friction with the axle. The radius isand each of the eight balls has a mass ofThe device is initially not rotating. A piece of clay falls and sticks to one of the balls as shown in the figure. The mass of the clay isand its speed just before the collision is
(a) Which of the following statements are true, for angular momentum relative to the axle of the wheel? (1) Just before the collision, (for the clay). (2) The angular momentum of the wheel is the same before and after the collision. (3) Just before the collision, the angular momentum of the wheel is. (4) The angular momentum of the wheel is the sum of the angular momentum of the wheel + clay after the collision is equal to the initial angular momentum of the clay. (6) The angular momentum of the falling clay is zero because the clay is moving in a straight line. (b) Just after the collision, what is the speed of one of the balls?
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 .
In Figure 11.95 two small objects each of mass \({m_1}\)are connected by a light weight rod of length \(L.\) At a particular instant the center of mass speed is\({v_1}\) as shown, and the object is rotating counterclockwise with angular speed \({\omega _1}\). A small object of mass \({m_2}\) travelling with speed \({v_2}\) collides with the rod at an angle \({\theta _2}\) as shown, at a distance\(b\)from the center of the rod. After being truck, the mass \({m_2}\) is observed to move with speed \({v_4}\) at angle\({\theta _4}\).All the quantities are positive magnitudes. This all takes place in outer space.
For the object consisting of the rod with the two masses, write equations that, in principle, could be solved for the center of mass speed \({v_3},\) direction \({\theta _3},\) and angular speed \({\omega _3}\)in terms of the given quantities. Sates clearly what physical principles you use to obtain your equations.
Don’t attempt to solve the equations; just set them up.
Redo the analysis, calculating torque and angular momentum relative to a fixed location in the ice anywhere underneath the string (similar to the analysis of the meter stick around one end). Show that the two analyses of the puck are consistent with each other.
A thin metal rod of mass and length is at rest in outer space, near a space station (Figure 11.99). A tiny meteorite with mass travelling at a high speed of strikes the rod a distance from the center and bounces off with speed 60 m/s as shown in the diagram. The magnitudes of initial and final angles to the of the small mass’s velocity are and .(a). Afterward, what is the velocity of the center of the rod? (b) Afterward, what is the angular velocity of the rod? (c) What is the increase in internal energy of the objects?
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