/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 16 It has been suggested that rotat... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Problem 16

It has been suggested that rotating cylinders about \(10 \mathrm{mi}\) long and \(5.0 \mathrm{mi}\) in diameter be placed in space and used as colonies. What angular speed must such a cylinder have so that the centripetal acceleration at its surface equals the free-fall acceleration on Earth?

Short Answer

Expert verified
The angular speed of the cylinder must be approximately 0.0495 rad/s.

Step by step solution

01

Transform given measures to SI units

Since the radius is half the diameter, its value is 2.5 mi which translates to 4023.36 meters (since 1 mile is approximately 1609.34 meters)
02

Formulate the equation for centripetal acceleration

The free fall acceleration on Earth \(a_c\) is given to be 9.8 \(m/s^2\). Thus the formula becomes \(a_{c} = \omega^2 \cdot r\) or \(9.8 = \omega^2 \cdot 4023.36\) incorporating the value of \(r\) we calculated earlier
03

Solve for the angular speed

To find the angular speed \(\omega\), we rearrange the equation and solve for \(\omega\): \(\omega^2 = \frac{a_{c}}{r} = \frac{9.8}{4023.36}\), so \(\omega = \sqrt{\frac{9.8}{4023.36}} = 0.0495 rad/s \)

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

(a) One of the moons of Jupiter, named Io, has an orbital radius of \(4.22 \times 10^{8} \mathrm{~m}\) and a period of \(1.77\) days. Assuming the orbit is circular, calculate the mass of Jupiter. (b) The largest moon of Jupiter, named Ganymede, has an orbital radius of \(1.07 \times 10^{9} \mathrm{~m}\) and a period of \(7.16\) days. Calculate the mass of Jupiter from this data. (c) Are your results to parts (a) and (b) consistent? Explain.

The tub of a washer goes into its spin-dry cycle, starting from rest and reaching an angular speed of 5.0 rev/s in \(8.0 \mathrm{~s}\). At this point, the person doing the laundry opens the lid, and a safety switch turns off the washer. The tub slows to rest in \(12.0 \mathrm{~s}\). Through how many revolutions does the tub turn during the entire 20 -s interval? Assume constant angular acceleration while it is starting and stopping.

A digital audio compact disc carries data along a continuous spiral track from the inner circumference of the disc to the outside edge. Each bit occupies \(0.6 \mu \mathrm{m}\) of the track. A CD player turns the disc to carry the track counterclockwise above a lens at a constant speed of \(1.30 \mathrm{~m} / \mathrm{s}\). Find the required angular speed (a) at the beginning of the recording, where the spiral has a radius of \(2.30 \mathrm{~cm}\), and (b) at the end of the recording, where the spiral has a radius of \(5.80 \mathrm{~cm}\). (c) A full-length recording lasts for \(74 \mathrm{~min}, 33 \mathrm{~s}\). Find the average angular acceleration of the disc. (d) Assuming the acceleration is constant, find the total angular displacement of the disc as it plays. (e) Find the total length of the track.

The tires on a new compact car have a diameter of \(2.0 \mathrm{ft}\) and are warranted for 60000 miles. (a) Determine the angle (in radians) through which one of these tires will rotate during the warranty period. (b) How many revolutions of the tire are equivalent to your answer in part (a)?

A sample of blood is placed in a centrifuge of radius \(15.0 \mathrm{~cm}\). The mass of a red blood cell is \(3.0 \times\) \(10^{-16} \mathrm{~kg}\), and the magnitude of the force acting on it as it settles out of the plasma is \(4.0 \times 10^{-11} \mathrm{~N}\). At how many revolutions per second should the centrifuge be operated?
See all solutions

Recommended explanations on Physics Textbooks

Nuclear Physics

Read Explanation

Turning Points in Physics

Read Explanation

Fluids

Read Explanation

Fundamentals of Physics

Read Explanation

Medical Physics

Read Explanation

Fields in Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.