College Physics
College Physics
11th Edition
ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
Bartleby Related Questions Icon

Related questions

bartleby

Concept explainers

Question
100%
[画像:### Circular Disk Kinematics Analysis #### Problem Statement Point A of the circular disk is at the angular position θ = 0 at time t = 0. The disk has angular velocity ω0 = 0.29 rad/s at t = 0 and subsequently experiences an angular acceleration α = 1.8t where t is in seconds, and α is in radians per second squared. Determine the velocity and acceleration of point A in terms of fixed i and j unit vectors at time t = 2.7 s. Assume r = 145 mm. #### Diagram Explanation A circular disk is depicted with: - Point \( O \) at its center. - A radius line \( r \) extending from \( O \) to point \( A \) on the circumference. - Angular position \( \theta \) measured counter-clockwise from the positive y-axis. - Angular acceleration \( \alpha \) shown counter-clockwise. #### Considerations 1. The radius \( r \) is given as 145 mm, which is equal to 0.145 m (after conversion to meters). 2. Initial angular velocity \( \omega_0 = 0.29 \) rad/s. 3. Angular acceleration \( \alpha = 1.8 t \). #### Formulas 1. **Angular Velocity** at time \( t \): \[ \omega(t) = \omega_0 + \int_0^t \alpha(t') dt' \] Given \( \alpha(t') = 1.8 t' \): \[ \omega(t) = 0.29 + \int_0^t 1.8 t' dt' = 0.29 + 1.8 \left( \frac{t^2}{2} \right) \] \[ \omega(t) = 0.29 + 0.9 t^2 \] 2. **Angle** at time \( t \): \[ \theta(t) = \omega_0 t + \int_0^t \omega(t') dt' \] Since: \[ \omega(t') = 0.29 + 0.9 t'^2 \] \[ \theta(t) = \int_0^t (0.29 + 0.9 t'^2) dt' = 0.29 t + 0.3 t^3 \] 3. **Velocity** of point \( A]
expand button
Transcribed Image Text:### Circular Disk Kinematics Analysis #### Problem Statement Point A of the circular disk is at the angular position θ = 0 at time t = 0. The disk has angular velocity ω0 = 0.29 rad/s at t = 0 and subsequently experiences an angular acceleration α = 1.8t where t is in seconds, and α is in radians per second squared. Determine the velocity and acceleration of point A in terms of fixed i and j unit vectors at time t = 2.7 s. Assume r = 145 mm. #### Diagram Explanation A circular disk is depicted with: - Point \( O \) at its center. - A radius line \( r \) extending from \( O \) to point \( A \) on the circumference. - Angular position \( \theta \) measured counter-clockwise from the positive y-axis. - Angular acceleration \( \alpha \) shown counter-clockwise. #### Considerations 1. The radius \( r \) is given as 145 mm, which is equal to 0.145 m (after conversion to meters). 2. Initial angular velocity \( \omega_0 = 0.29 \) rad/s. 3. Angular acceleration \( \alpha = 1.8 t \). #### Formulas 1. **Angular Velocity** at time \( t \): \[ \omega(t) = \omega_0 + \int_0^t \alpha(t') dt' \] Given \( \alpha(t') = 1.8 t' \): \[ \omega(t) = 0.29 + \int_0^t 1.8 t' dt' = 0.29 + 1.8 \left( \frac{t^2}{2} \right) \] \[ \omega(t) = 0.29 + 0.9 t^2 \] 2. **Angle** at time \( t \): \[ \theta(t) = \omega_0 t + \int_0^t \omega(t') dt' \] Since: \[ \omega(t') = 0.29 + 0.9 t'^2 \] \[ \theta(t) = \int_0^t (0.29 + 0.9 t'^2) dt' = 0.29 t + 0.3 t^3 \] 3. **Velocity** of point \( A
Expert Solution
Check Mark
Knowledge Booster
Background pattern image
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
    Text book image
    College Physics
    Physics
    ISBN:9781305952300
    Author:Raymond A. Serway, Chris Vuille
    Publisher:Cengage Learning
    Text book image
    University Physics (14th Edition)
    Physics
    ISBN:9780133969290
    Author:Hugh D. Young, Roger A. Freedman
    Publisher:PEARSON
    Text book image
    Introduction To Quantum Mechanics
    Physics
    ISBN:9781107189638
    Author:Griffiths, David J., Schroeter, Darrell F.
    Publisher:Cambridge University Press
    Text book image
    Physics for Scientists and Engineers
    Physics
    ISBN:9781337553278
    Author:Raymond A. Serway, John W. Jewett
    Publisher:Cengage Learning
    Text book image
    Lecture- Tutorials for Introductory Astronomy
    Physics
    ISBN:9780321820464
    Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
    Publisher:Addison-Wesley
    Text book image
    College Physics: A Strategic Approach (4th Editio...
    Physics
    ISBN:9780134609034
    Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
    Publisher:PEARSON