Homework Help is Here – Start Your Trial Now!
Science
Physics
Analyzing circular motion at constant speed is an important next step after you've developed an ability to explain motions with constant acceleration (like free fall). The peculiarity of circular motion at constant speed is that the magnitude of the acceleration is constant, but the direction of the acceleration vector rotates so that it always points to the center of the circle. It's completely different than "free fall", where the acceleration's direction points down and doesn't rotate. Rotating acceleration is illustrated in the top figure. Two velocity vectors are shown: V₁ and v2. They indicate the velocities at the two ends of an arc. They have the same length v, which matches the constant speed idea. The direction changes as the ball moves around. When you subtract one vector from the other, the difference is the "velocity change vector". It always points towards the center of the circle from the middle of the arc. The "centripetal acceleration" has the magnitude a centripetal =V²/r anywhere on the circle. V2 Av Velocity change vector: Av=V₂ - V₁ r 121 V1 Sog h Swing rides at amusement parks are a popular way to experience this type of motion. The photograph captures a swing ride in motion. You can see a series of cables swung out from the top disk at an angle. At the end of each cable is a seat with a person riding the swing. The riders travel around a circle - it's fun! A swing ride is one example of a "conical pendulum". In the photograph, the lines of the cables from all the seats intersect at a vertex above the disk, and these lines form the cone. As you might expect, when the ride turns faster, the angle at the vertex of the cone gets larger. The radius of the circle also gets bigger. The vertical distance h from the vertex down to the chairs

Analyzing circular motion at constant speed is an important next step after you've developed an ability to explain motions with constant acceleration (like free fall). The peculiarity of circular motion at constant speed is that the magnitude of the acceleration is constant, but the direction of the acceleration vector rotates so that it always points to the center of the circle. It's completely different than "free fall", where the acceleration's direction points down and doesn't rotate. Rotating acceleration is illustrated in the top figure. Two velocity vectors are shown: V₁ and v2. They indicate the velocities at the two ends of an arc. They have the same length v, which matches the constant speed idea. The direction changes as the ball moves around. When you subtract one vector from the other, the difference is the "velocity change vector". It always points towards the center of the circle from the middle of the arc. The "centripetal acceleration" has the magnitude a centripetal =V²/r anywhere on the circle. V2 Av Velocity change vector: Av=V₂ - V₁ r 121 V1 Sog h Swing rides at amusement parks are a popular way to experience this type of motion. The photograph captures a swing ride in motion. You can see a series of cables swung out from the top disk at an angle. At the end of each cable is a seat with a person riding the swing. The riders travel around a circle - it's fun! A swing ride is one example of a "conical pendulum". In the photograph, the lines of the cables from all the seats intersect at a vertex above the disk, and these lines form the cone. As you might expect, when the ride turns faster, the angle at the vertex of the cone gets larger. The radius of the circle also gets bigger. The vertical distance h from the vertex down to the chairs

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
See similar textbooks
icon
Related questions
Question
**Features of a Pre-lab Homework** Analyzing circular motion at constant speed is an important next step after you’ve developed an ability to explain motions with constant acceleration (like free fall). The peculiarity of circular motion at constant speed is that the magnitude of the acceleration is constant, but the direction of the acceleration vector rotates so that it always points to the center of the circle. It’s completely different than “free fall”, where the acceleration’s direction points down and doesn’t rotate. Rotating acceleration is illustrated in the top figure. Two velocity vectors are shown: \(v_1\) and \(v_2\). They indicate the velocities at the two ends of an arc. They have the same length \(v\), which matches the constant speed idea. The direction changes as the ball moves around. When you subtract one vector from the other, the difference is the “velocity change vector”. It always points towards the center of the circle from the middle of the arc. The “centripetal acceleration” has the magnitude \(a_{\text{centripetal}} = v^2/r\) anywhere on the circle. Swing rides at amusement parks are a popular way to experience this type of motion. The photograph captures a swing ride in motion. You can see a series of cables swung out from the top disk at an angle. At the end of each cable is a seat with a person riding the swing. The riders travel around a circle - it’s fun! A swing ride is one example of a “conical pendulum”. In the photograph, the lines of the cables from all the seats intersect at a vertex above the disk, and these lines form the cone. As you might expect, when the ride turns faster, the angle at the vertex of the cone gets larger. The radius of the circle also gets bigger. The vertical distance \(h\) from the vertex down to the chairs gets smaller. In terms of \(h\), the equation for the time \(T\) that it takes a rider to do one circle is \(T = 2\pi \sqrt{h/g}\), where \(g\) is the gravitational acceleration constant (about 9.8 \(m/s^2\)). It’s interesting that the equation is the same for the period of an ordinary pendulum of length \(h\) that just swings back and forth. It isn’t a coincidence, but we won’t go further. The speed \(s
Transcribed Image Text:**Features of a Pre-lab Homework** Analyzing circular motion at constant speed is an important next step after you’ve developed an ability to explain motions with constant acceleration (like free fall). The peculiarity of circular motion at constant speed is that the magnitude of the acceleration is constant, but the direction of the acceleration vector rotates so that it always points to the center of the circle. It’s completely different than “free fall”, where the acceleration’s direction points down and doesn’t rotate. Rotating acceleration is illustrated in the top figure. Two velocity vectors are shown: \(v_1\) and \(v_2\). They indicate the velocities at the two ends of an arc. They have the same length \(v\), which matches the constant speed idea. The direction changes as the ball moves around. When you subtract one vector from the other, the difference is the “velocity change vector”. It always points towards the center of the circle from the middle of the arc. The “centripetal acceleration” has the magnitude \(a_{\text{centripetal}} = v^2/r\) anywhere on the circle. Swing rides at amusement parks are a popular way to experience this type of motion. The photograph captures a swing ride in motion. You can see a series of cables swung out from the top disk at an angle. At the end of each cable is a seat with a person riding the swing. The riders travel around a circle - it’s fun! A swing ride is one example of a “conical pendulum”. In the photograph, the lines of the cables from all the seats intersect at a vertex above the disk, and these lines form the cone. As you might expect, when the ride turns faster, the angle at the vertex of the cone gets larger. The radius of the circle also gets bigger. The vertical distance \(h\) from the vertex down to the chairs gets smaller. In terms of \(h\), the equation for the time \(T\) that it takes a rider to do one circle is \(T = 2\pi \sqrt{h/g}\), where \(g\) is the gravitational acceleration constant (about 9.8 \(m/s^2\)). It’s interesting that the equation is the same for the period of an ordinary pendulum of length \(h\) that just swings back and forth. It isn’t a coincidence, but we won’t go further. The speed \(s
Problem Scaling from the photograph and the seated size of the riders, \( h \) is about 12 meters and \( r \) is about 9 meters. (a) What is the period \( T \) of the swing ride? (b) What is the speed \( s \) at which the riders are moving? (c) What is the ratio of the centripetal acceleration of the riders and the gravitational acceleration \( g \)?
Transcribed Image Text:Problem Scaling from the photograph and the seated size of the riders, \( h \) is about 12 meters and \( r \) is about 9 meters. (a) What is the period \( T \) of the swing ride? (b) What is the speed \( s \) at which the riders are moving? (c) What is the ratio of the centripetal acceleration of the riders and the gravitational acceleration \( g \)?
Expert Solution
Step 1: Height and radius of the circular wheel is given

Height h = 12m

Radius r = 9m


steps

Step by step

Solved in 3 steps with 5 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Centripetal force
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
College Physics
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
Physics for Scientists and Engineers
Physics for Scientists and Engineers
Physics
ISBN:
9781337553278
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:
9780321820464
Author:
Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:
Addison-Wesley
College Physics: A Strategic Approach (4th Editio…
College Physics: A Strategic Approach (4th Editio…
Physics
ISBN:
9780134609034
Author:
Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:
PEARSON
SEE MORE TEXTBOOKS