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What is the angular speed (in rev / min) of the Earth as it orbits about the Sun?

Short Answer

Expert verified
The Earth's angular speed around the Sun is approximately \(1.9025 \times 10^{-6}\) rev/min.

Step by step solution

01

Identify the Known Values

To find the angular speed of the Earth as it orbits the Sun, we firstly recognize that the Earth completes one full orbit around the Sun in approximately 365.25 days. Each complete orbit represents 1 revolution.
02

Convert Time Period to Minute Units

Since the question asks for the angular speed in revolutions per minute, convert the orbital period of the Earth from days to minutes. We know there are 24 hours in a day, and 60 minutes in an hour, therefore:\[\text{Total minutes in one year} = 365.25 \text{ days} \times 24 \text{ hours/day} \times 60 \text{ minutes/hour}\]This results in 525,960 minutes per year.
03

Calculate Angular Speed in Revolutions per Minute

Angular speed \( \omega \) in revolutions per minute is defined as the number of revolutions divided by the time period in minutes:\[\omega = \frac{\text{Number of Revolutions}}{\text{Time Period in Minutes}} = \frac{1 \text{ revolution}}{525,960 \text{ minutes}}\]This simplifies to approximately \(1.9025 \times 10^{-6}\) revolutions per minute.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Earth's orbit
The Earth's orbit around the Sun is a fascinating journey that takes roughly a year to complete. In astronomical terms, one full trip around our central star is known as a revolution. During this period, Earth travels on an elliptical path, which is almost circular, making it remarkably consistent.
Many might wonder why it takes about 365.25 days for Earth to orbit the Sun. This fractional day accounts for the extra effort our calendar system takes to keep up with astronomical events, which is why we have a leap year every four years to synchronize time keeping with celestial movements.
Understanding how Earth orbits the Sun helps us appreciate not just the length of a year, but also the majestic design of our solar system's mechanics. It is this predictable path that leads to seasons, changes in climate, and the day-night cycle.
revolutions per minute
To measure Earth's motion in terms of revolutions per minute (rev/min), think of it as breaking down a grand cosmic journey into a miniscule timeframe. Even though the Earth takes a year for a single revolution around the Sun, we can find out how much of that revolution occurs each minute.
Angular speed is a way to quantify this motion. It describes how quickly an object travels around a circle. For the Earth, its angular speed as it orbits the Sun is relatively slow when expressed in revolutions per minute because of the enormity of its path and the vast number of minutes in a year.
This measurement gives us an ultra-specific glance into Earth's journey, enhancing our understanding of both celestial mechanics and the passage of time.
orbital period conversion
Converting the orbital period from days to minutes is an essential step for calculating Earth's angular speed. It's important to break this down clearly. Firstly, know that there are 24 hours in a day and 60 minutes in an hour, which means changing days into minutes involves simple multiplication.
Given Earth's orbital period is about 365.25 days, multiply 365.25 by 24 and then by 60. This results in approximately 525,960 minutes per year. This conversion is the backbone of determining how Earth's revolution translates into angular speed.
Understanding this conversion process is crucial, as it helps you translate larger celestial timeframes into smaller, more manageable units, a process widely used in various scientific applications.

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Most popular questions from this chapter

The angular speed of a propeller on a boat increases with constant acceleration from 11 rad/s to 28 rad/s in 2.4 seconds. Through what angle did the propeller turn during this time?

The drill used by most dentists today is powered by a small air turbine that can operate at angular speeds of 350,000 rpm. These drills, along with ultrasonic dental drills, are the fastest turbines in the world-far exceeding the angular speeds of jet engines. Suppose a drill starts at rest and comes up to operating speed in \(2.1 \mathrm{s}\). (a) Find the angular acceleration produced by the drill, assuming it to be constant. (b) How many revolutions does the drill bit make as it comes up to speed?

A yo-yo moves downward until it reaches the end of its string, where it "sleeps." As it sleeps-that is, spins in place-its angular speed decreases from \(35 \mathrm{rad} / \mathrm{s}\) to \(25 \mathrm{rad} / \mathrm{s}\) During this time it completes 120 revolutions. (a) How long did it take for the yo-yo to slow from \(35 \mathrm{rad} / \mathrm{s}\) to \(25 \mathrm{rad} / \mathrm{s} ?\) (b) How long does it take for the yo-yo to slow from \(25 \mathrm{rad} / \mathrm{s}\) to 15 rad / s? Assume a constant angular acceleration as the yoyo sleeps.

When you stand on the observation deck of the Empire State Building in New York, is your linear speed due to the Earth's rotation greater than, less than, or the same as when you were waiting for the elevators on the ground floor?

The moment of inertia of a 0.98 -kg bicycle wheel rotating about its center is \(0.13 \mathrm{kg} \cdot \mathrm{m}^{2}\). What is the radius of this wheel, assuming the weight of the spokes can be ignored?

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