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Chapter 8: 8-3P (page 198)

A laser beam is directed at the Moon, 380,000 km from Earth. The beam diverges at an angle \({\bf{\theta }}\) (Fig. 8鈥�40) of \({\bf{1}}{\bf{.4 \times 1}}{{\bf{0}}^{{\bf{ - 5}}}}\;{\bf{rad}}\). What diameter spot will it make on the Moon?

FIGURE 8-40 Problem 3.

Short Answer

Expert verified

The diameter of the circular spot that formed on the surface of the Moon is \(5.3 \times {10^3}\;{\rm{m}}\).

Step by step solution

01

Meaning of angular motion

The angular motion includes the circular or rotational motion of an object. The circular motion can be estimated using linear units or angular units.

The angular units refer to revolutions, radians, and degrees.

02

Given information

Given data:

The distance between the Earth and the Moon is \(r = 380000\;{\rm{km}}\).

The diverging angle is \(\theta = 1.4 \times {10^{ - 5}}\;{\rm{rad}}\).

03

Calculate the diameter of the spot

The diameter of the spot can be calculated as:

\(\begin{aligned}{l}d &= r\theta \\d &= \left( {\left( {380000\;{\rm{km}}} \right)\left( {\frac{{{\rm{1}}{{\rm{0}}^{\rm{3}}}\;{\rm{m}}}}{{{\rm{1}}\;{\rm{km}}}}} \right)} \right)\left( {1.4 \times {{10}^{ - 5}}\;{\rm{rad}}} \right)\\d &= 5.3 \times {10^3}\;{\rm{m}}\end{aligned}\)

Thus, the diameter of the circular spot that formed on the surface of the Moon is \(5.3 \times {10^3}\;{\rm{m}}\).

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Most popular questions from this chapter

Question:(II) A person stands, hands at his side, on a platform that is rotating at a rate of 0.90 rev/s. If he raises his arms to a horizontal position, Fig. 8鈥�55, the speed of rotation decreases to 0.60 rev/s. (a) Why? (b) By what factor has his moment of inertia changed?

A large spool of rope rolls on the ground with the end of the rope lying on the top edge of the spool. A person grabs the end of the rope and walks a distance l, holding onto it, Fig. 8鈥�64. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far does the spool鈥檚 center of mass move?

Question:(II) A diver (such as the one shown in Fig. 8鈥�28) can reduce her moment of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular speed (rev/s) when in the straight position?

An oxygen molecule consists of two oxygen atoms whose total mass is \({\bf{5}}{\bf{.3 \times 1}}{{\bf{0}}^{{\bf{ - 26}}}}\;{\bf{kg}}\) and the moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is \({\bf{1}}{\bf{.9 \times 1}}{{\bf{0}}^{{\bf{ - 46}}}}\;{\bf{kg}} \cdot {{\bf{m}}^{\bf{2}}}\). From these data, estimate the effective distance between the atoms.

A car speedometer that is supposed to read the linear speed of the car uses a device that actually measures the angular speed of the tires. If larger-diameter tires are mounted on the car instead, how will that affect the speedometer reading? The speedometer

(a) will still read the speed accurately.

(b) will read low.

(c) will read high
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