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Chapter 11: Q1CP (page 418)

What is the direction of the orbital (translational) angular momentum of the comet shown in the figure relative to the Sun?

Short Answer

Expert verified

Direction of angular momentum is in negative Z- direction.

Step by step solution

01

Definition of Angular Momentum

Angular momentum is a measure of rotational motion.

Translational (or “orbital”) angular momentum describes motion such as the orbit of the Earth around the Sun. Rotational (or "spin") angular momentum describes motion such as the revolution of the Earth around its own axis.

Momentum Principle relates a change in momentum to the net force on a system, the Angular Momentum Principle relates a change in angular momentum to the net torque, or twist, applied to a system.

02

Direction of Comet relative to Sun

Applying the right-hand rule, the comet's translational angular momentum shown in fig.1 is in the negative z direction: inwards the page.

Fig.1

Therefore, the direction of angular momentum is in negative Z- direction.

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Most popular questions from this chapter

Pinocchio rides a horse on a merry-go-round turning counterclockwise as viewed from above, with his long nose always pointing forwards, in the direction of his velocity. Is Pinocchio’s translational angular momentum relative to the center of the merry-go-round zero or nonzero? In nonzero, what is its direction? Is his rational angular momentum zero or nonzero? If nonzero, what is its direction?

The moment of inertia of a sphere of uniform density rotating on its axis is \(\frac{2}{5}M{R^2}\). Use data given at the end of this book to calculate the magnitude of the rotational angular momentum of the Earth.

Two people of different masses sit on a seesaw (Figure 11.103). M1,the mass of personis90kg,M2is42kg,d1=0.8m,andd2=1.3m.The people are initially at rest. The mass of the board is negligible.

(a) What are the magnitude and direction of the torque about the pivot due to the gravitational force on person(b) What are the magnitude and direction of the torque about the pivot due to the gravitational force on person(c) Since at this instant the linear momentum of the system may be changing, we don’t known the magnitude of the “normal” force exerted by the pivot. Nonetheless, it is possible to calculate the torque due to this force. What are the magnitude and direction of the torque about the pivot due to the force exerted by the pivot on the board? (d) What are the magnitude and direction of the net torque on the system (board + people)? (e) Because of this net torque, what will happen? (A) The seesaw will begin to rotate clockwise. (B) The seesaw will begin to rotate counterclockwise. (C) The seesaw will not move. (f) Person 2 moves to a new position, in which the magnitude of the net torque about the pivot is now0,and the seesaw is balanced. What is the new value ofd2in this situation?

In Figure11.89depicts a device that can rotate freely with little friction with the axle. The radius is0.4m,and each of the eight balls has a mass of0.3kg.The 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 is0.066kgand its speed just before the collision is10m/s.

(a) Which of the following statements are true, for angular momentum relative to the axle of the wheel? (1) Just before the collision, r⊥=0.42/2=0.4cos(45°)(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 is0. (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 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 ⟨-0.36,0.480,0⟩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.
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