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Chapter 11: Q1Q (page 458)

Give an example of a situation in which an object is traveling a straight line, yet has non-zero angular momentum.

Short Answer

Expert verified

The angular momentum of the spacecraft relative to the asteroid has non-zero value.

Step by step solution

01

Definition of Angular Momentum

The angular momentum is a characteristic that describes an object or a system of items' rotational inertia in motion around an axis that may or may not pass through the object or system.

02

The example of a situation is-

A straight-moving spaceship passing an asteroid is an example of an object moving in a straight line with angular momentum greater than zero.

The situation is shown in the following figure.

Hence, the angular momentum of the spacecraft relative to the asteroid has non-zero value.

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Most popular questions from this chapter

In figure two small objects each of mass $m = 0.3 k g$ are connected by a lightweight rod of length $d = 1.5 m .$ At a particular instant they have velocities whose magnitude are $v_{1} = 38 m / s$ and $v_{2} = 60 m / s$ and are subjected to external forces whose magnitudes are $F_{1} = 41 N$ and $F_{2} = 26 N$ . The distance role="math" localid="1668661918159" $h = 0.3 m,$ and the distance $w = 0.7 m .$ The system is moving in outer space. Assuming the usual coordinate system with $+ x$ to the right, $+ y$ toward the top of the page, and $+ z$ out of the page toward you, calculated these quantities for this system:

(a) ${\vec{p}}_{t o t a l,}$ (b) ${\vec{v}}_{C M,}$ (c) ${\vec{L}}_{t o t, A,}$ (d) ${\vec{L}}_{r o t,}$ (e) ${\vec{L}}_{t r a n s A,}$ (f) ${\vec{P}}_{t o t a l}$ at a time $0.23 s$ after the initial time.

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 $20 s$ In 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 mass $40 k g$ , 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 $\vec{L} = \vec{r} \times \vec{p},$ what is the vector $\vec{r}$ ? (c) what is $\vec{r} ⊥$ ? (d) what is the magnitude of the angular momentum of the child about location $A$ ? (e) What is the plane defined by $\vec{r} a n d \vec{p}$ (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 location $A$ . (g) You used the right-hand rule to determine the $z$ component of the angular momentum, but as a check, calculate in terms of position and momentum: What is $y p_{x}$ ? Therefore, what is $z$ the component of the angular momentum of the child about location $A$ ? (h) The Ferris wheel keeps turning, and at a later time, the same child is at location $E$ with 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 $A$ ?

In Figure 11.96a spherical non-spinning asteroid of mass\(M\)and radius\(R\)moving with speed\({v_1}\)to the right collides with a similar non-spinning asteroid moving with speed\({v_2}\)to the left, and they stick together. The impact parameter is\(d\).Note that\({I_{sphere}} = \frac{2}{5}M{R^2}.\)

After the collision, what is the velocity \({v_{CM}}\) of the center of mass and the angular velocity \(\omega \) about the center of mass? (Note that each asteroid rotates about its own center with this same \(\omega \)).

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?

If you did not already do problem P63 do it now. Also calculate numerically the angle through which the apparatus turns, in radians and degrees.

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