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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 rotating uniform-density disk of radius 0.6mis mounted in the vertical plane, as shown in Figure 11.88.The axle is held up by supports that are not shown, and the disk is free to rotate on the nearly frictionless axle. The disk has mass 5kg.A lump of clay with mass0.4kgfalls and sticks to the outer edge of the wheel at the location 鉄�-0.36,0.480,0鉄�m,relative to an origin at the centre of the axle. Just before the impact the clay has speed 8m/s,and the disk is rotating clockwise with angular speed0.51radians/s.

(a) Just before the impact, what is the angular momentum (magnitude and direction) of the combined system of wheel plus clay about the centerC?(As usual,xis to the right,yis up, andzis out of the screen, toward you.) (b) Just after the impact, what is the angular momentum (magnitude and direction) of the combined system of wheel plus clay about the centerC?(c) Just after the impact, what is the angular velocity (magnitude and direction) of the wheel? (d) Qualitatively, what happens to the linear momentum of the combined system? Why? (A) There is no change because linear momentum is always conserved. (B) Some of the linear momentum is changed into angular momentum. (C) Some of the linear momentum is changed into energy. (D) The downward linear momentum decreases because the axle exerts an upward force.

In figure two small objects each of mass m=0.3kgare connected by a lightweight rod of length d=1.5m.At a particular instant they have velocities whose magnitude are v1=38m/sand v2=60m/sand are subjected to external forces whose magnitudes are F1=41NandF2=26N. The distance role="math" localid="1668661918159" h=0.3m,and the distancew=0.7m.The system is moving in outer space. Assuming the usual coordinate system with+xto the right, +ytoward the top of the page, and +zout of the page toward you, calculated these quantities for this system:

(a) p鈫�total,(b) v鈫�CM, (c) L鈫�tot,A, (d)L鈫�rot,(e) L鈫�transA, (f) P鈫�totalat a time 0.23s after the initial time.

Calculate the angular momentum for a rotating disk, sphere, and rod: (a) A uniform disk of mass 13kg, thickness 0.5mand radius0.2mis located at the origin, oriented with its axis along they axis. It rotates clockwise around its axis when viewed form above (that is, you stand at a point on the +y axis and look toward the origin at the disk). The disk makes one complete rotation every0.6s . What is the rotational angular momentum of the disk? What is the rotational kinetic energy of the disk? (b) A sphere of uniform density, with mass22kg and radius0.7m is located at the origin and rotates around an axis parallel with thex axis. If you stand somewhere on the +xaxis and look toward the origin at the sphere, the sphere spins counterclockwise. One complete revolution takes0.5s .What is the rotational angular momentum of the sphere? What is the rotational kinetic energy of the sphere? (c) A cylindrical rod of uniform density is located with its center at the origin, and its axis along thez axis. Its radius is0.06m its length is0.7m and its mass is 5kgIt makes one revolution every 0.03sIf you stand on the +xaxis and look toward the origin at the rod, the rod spins clockwise. What is the rotational angular momentum of the rod? What is the rotational kinetic energy of the rod?

As shown in figure, seven forces all with magnitude \(\left| {\overrightarrow F } \right| = 25{\rm{ N}}\) are applied to an irregularly shaped object. Each force is applied at a different location on the object, indicated by the tail of the arrow; the directions of the force differ. The distances shown in the diagram have these values: \(w = 9{\rm{ m}},{\rm{ }}h = 14{\rm{ m}}\)and\(d = 13{\rm{ m}}\). For each force, calculate the \(z\)-component of the torque due to that force, relative to location A (\(x\) to the right, \(y\)up, \(z\) out of the page). Make sure you give the correct sign. Relative to location A, what is the \(z\) component of the net torque acting this object?

What are the units of moment of inertia? Of angular speed 蝇? Of angular momentum? Of linear momentum?
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