/*! 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 8 A wheel is rotating at a rate of... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 8

A wheel is rotating at a rate of 2.0 revolutions every \(3.0 \mathrm{s} .\) Through what angle, in radians, does the wheel rotate in \(1.0 \mathrm{s} ?\)

Short Answer

Expert verified
Answer: The wheel rotates \(\frac{4}{3}\pi\) radians in 1.0 seconds.

Step by step solution

01

Calculate the rate per second

First, we need to find out how many revolutions the wheel makes per second. Divide the number of revolutions by the given time to obtain the revolutions per second: Rate (revolutions per second) \(= \frac{2.0\,\text{revolutions}}{3.0\,\text{seconds}}\).
02

Simplify the rate

Now, simplify the fraction to get the rate as a simplified number: Rate (revolutions per second) \(= \frac{2}{3}\,\text{revolutions/s}\).
03

Convert revolutions to radians

In one full revolution, a wheel makes an angle of \(2 \pi\) radians. To convert the rate in revolutions/s to radians/s, simply multiply the rate by \(2\pi\): Rate (radians per second) \(= \frac{2}{3} \times 2\pi\,\text{radians/s}\).
04

Calculate the angle in 1 second

Now that we have the rate in radians per second, we can find the angle the wheel rotates in 1.0 seconds by multiplying the rate in radians/s by 1.0 seconds: Angle rotated in 1 second \(= \frac{2}{3}\times 2\pi\,\text{radians/s} \times 1.0\,\text{s}\).
05

Simplify the result

Perform the multiplication, simplifying the expression to obtain the final answer: Angle rotated in 1 second \(= \frac{4}{3}\pi\,\text{radians}\).

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 coin is placed on a turntable that is rotating at 33.3 rpm. If the coefficient of static friction between the coin and the turntable is \(0.1,\) how far from the center of the turntable can the coin be placed without having it slip off?
Two satellites are in circular orbits around Jupiter. One, with orbital radius \(r,\) makes one revolution every \(16 \mathrm{h}\) The other satellite has orbital radius \(4.0 r .\) How long does the second satellite take to make one revolution around Jupiter?

A biologist is studying growth in space. He wants to simulate Earth's gravitational field, so he positions the plants on a rotating platform in the spaceship. The distance of each plant from the central axis of rotation is \(r=0.20 \mathrm{m} .\) What angular speed is required?
Mars has a mass of about \(6.42 \times 10^{23} \mathrm{kg} .\) The length of a day on Mars is \(24 \mathrm{h}\) and 37 min, a little longer than the length of a day on Earth. Your task is to put a satellite into a circular orbit around Mars so that it stays above one spot on the surface, orbiting Mars once each Mars day. At what distance from the center of the planet should you place the satellite?
A jogger runs counterclockwise around a path of radius \(90.0 \mathrm{m}\) at constant speed. He makes 1.00 revolution in 188.4 s. At \(t=0,\) he is heading due east. (a) What is the jogger's instantaneous velocity at $t=376.8 \mathrm{s} ?\( (b) What is his instantaneous velocity at \)t=94.2 \mathrm{s} ?$
See all solutions

Recommended explanations on Physics Textbooks

Translational Dynamics

Read Explanation

Further Mechanics and Thermal Physics

Read Explanation

Geometrical and Physical Optics

Read Explanation

Famous Physicists

Read Explanation

Nuclear 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.