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Chapter 11: Q5Q (page 458)

Give an example of physical situation in which the angular momentum is zero yet the translational and rotational angular momenta are both non-zero.

Short Answer

Expert verified

A spacecraft carrying a gyroscope is the best example of this physical situation.

Step by step solution

01

Definition of Angular momentum and rotational angular momentum

The rotating inertia of an object or system of objects in motion about an axis that may or may not pass through the object or system is described by angular momentum.

The rotating analog of linear momentum is angular momentum (also known as moment of momentum or rotational momentum). A closed system's total angular momentum remains constant.

02

Step 2:The figure of Spacecraft carries a gyroscope

A spacecraft carries a gyroscope that is not spinning as shown in the following figure.

03

Principal of Spacecraft carries a gyroscope

A gyroscope aboard a spacecraft is the greatest example of this physical scenario. Assume that the spaceship has a non-rotating gyroscope, as shown in the diagram. In this situation, the spacecraft's angular momentum around its center of mass is zero. If the gyroscope is rotated, it has an angular momentum greater than zero. Because the isolated system (spacecraft + gyroscope) has no external torque, the angular momentum of the system must remain zero according to the principle of conservation of angular momentum.

This principle can only be satisfied if the spacecraft rotates in the opposite direction as the gyroscope, causing the angular momentum vectors of the gyroscope and spacecraft to cancel, leaving the system with no angular momentum. The spacecraft turns around as a result of rotating the gyroscope, as seen in the diagram above.

As a result, the spacecraft's gyroscope is an excellent example of this physical scenario.

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Most popular questions from this chapter

A common amusement park ride is a Ferris wheel (see figure, which is not drawn to scale). Riders sit in chairs that are on pivots so they remain level as the wheel turns at a constant rate. A particular Ferris wheel has a radius of 24 meters, and it make one complete revolution around its axle (at location A) in 20sIn all of the following questions, consider location A(at the center of the axle) as the location around which we will calculate the angular momentum. At the instant shown in the diagram, a child of mass40kg, sitting at location F, is traveling with velocity <7.5,0,0>m/s.

(a.) What is the linear momentum of the child? (b) In the definition L鈫�=r鈫�脳p鈫�,what is the vector r鈫�? (c) what is r鈫�鈯�? (d) what is the magnitude of the angular momentum of the child about location A? (e) What is the plane defined by r鈫�andp鈫�(that is, the plane containing both of these vectors)? (f) Use the right-hand rule to determine thecomponent of the angular momentum of the child about locationA. (g) You used the right-hand rule to determine the zcomponent of the angular momentum, but as a check, calculate in terms of position and momentum: What isypx? Therefore, what iszthe component of the angular momentum of the child about locationA? (h) The Ferris wheel keeps turning, and at a later time, the same child is at locationEwith coordinates<16.971,-16.971,0>m relative to location A, moving with velocity<5.303,5.303,0>m/s.Now what is the magnitude of the angular momentum of the child about location A?

An amusing trick is to press a finger down on a marble on a horizontal table top, in such a way that the marble is projected along the table with an initial linear speed vand an initial backward rotational speed 蝇about a horizontal axis perpendicular to v. The coefficient of sliding friction between marble and top is constant. The marble has radius R. (a) if the marble slides to a complete stop, What was 蝇in terms of vandR? (b) if the marble, skids to a stop, and then starts returning toward its initial position, with a final constant speed of (3/7)v,What was 蝇in terms of vandR? Hint for part (b): when the marble rolls without slipping, the relationship between speed and angular speed isv=蝇R.

A yo-yo is constructed of three disks: two outer disks of mass M, radius R, and thickness d, and an inner disk (around which the string is wrapped) of mass , radius , and thickness d. The yo-yo is suspended from the ceiling and then released with the string vertical (figure).

Calculate the tension in the string as the yo-yo falls. Note that when the center of the yo-yo moves down a distance y, the yo-yo turns through an angley/r,which in turn means that the angular speed蝇is equal to vCM/r. The moment of inertia of a uniform disk is12MR2.

Under what conditions is the torque about some location equal to zero?

A barbell is mounted on a nearly frictionless axle through its center (Figure 11.105). At this instant, there are two forces of equal magnitude applied to the system as shown, with the directions indicated, and at this instant, the angular velocity is 60 Rad/s, counterclockwise. In the next 0.001s,the angular momentum relative to the center increases by an amount 2.5 kg.meter square per second. What is the magnitude of each force? What is the net force?
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