A child is pushing a merry-go-round. The angle through which the merry-go-round has turned varies with time according to 8(t)=yt + Bt³. where y=0.390 rad/s and B=0.0130 rad/s³. For related problem-solving tips and strategies, you may want to view a Video Tutor Solution of Calculating angular velocity. ♥ ▼ Part A Calculate the angular velocity of the merry-go-round as a function of time. Express your answer in terms of the variables,, and rad/s. G| ΑΣΦ w₂(t) = Submit Part B What is the initial value of the angular velocity? Express your answer in radians per second. 15] ΑΣΦ W₂ = Submit Request Answer Part C Request Answer ? ? rad/s Calculate the instantaneous value of the angular velocity w, at t= 5.40 s. Express your answer in radians per second.
A child is pushing a merry-go-round. The angle through which the merry-go-round has turned varies with time according to 8(t)=yt + Bt³. where y=0.390 rad/s and B=0.0130 rad/s³. For related problem-solving tips and strategies, you may want to view a Video Tutor Solution of Calculating angular velocity. ♥ ▼ Part A Calculate the angular velocity of the merry-go-round as a function of time. Express your answer in terms of the variables,, and rad/s. G| ΑΣΦ w₂(t) = Submit Part B What is the initial value of the angular velocity? Express your answer in radians per second. 15] ΑΣΦ W₂ = Submit Request Answer Part C Request Answer ? ? rad/s Calculate the instantaneous value of the angular velocity w, at t= 5.40 s. Express your answer in radians per second.
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)...
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![### Understanding Angular Velocity
A child is pushing a merry-go-round. The angle through which the merry-go-round has turned varies with time according to the equation:
\[
\theta(t) = \gamma t + \beta t^3
\]
where \(\gamma = 0.390 \, \text{rad/s}\) and \(\beta = 0.0130 \, \text{rad/s}^3\).
For related problem-solving tips and strategies, you may want to view a Video Tutor Solution on [Calculating Angular Velocity](#).
---
#### Part A
**Task:**
Calculate the angular velocity of the merry-go-round as a function of time.
Express your answer in terms of the variables \(\gamma\), \(\beta\), \(t\), and \(\text{rad/s}\).
Input field for equation:
\(\omega(t) = \)
---
#### Part B
**Task:**
What is the initial value of the angular velocity?
Express your answer in radians per second.
Input field for equation:
\(\omega_i = \) \(\text{rad/s}\)
---
#### Part C
**Task:**
Calculate the instantaneous value of the angular velocity \(\omega\) at \(t = 5.40 \, \text{s}\).
Express your answer in radians per second.
Input field for equation:
\(\omega = \) \(\text{rad/s}\)
---](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F76eec8ec-d87c-4fdd-96a3-96e8325f09a2%2F961e0fbb-c36d-4876-9cea-277e3fb721fa%2Fia97ybu_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Understanding Angular Velocity
A child is pushing a merry-go-round. The angle through which the merry-go-round has turned varies with time according to the equation:
\[
\theta(t) = \gamma t + \beta t^3
\]
where \(\gamma = 0.390 \, \text{rad/s}\) and \(\beta = 0.0130 \, \text{rad/s}^3\).
For related problem-solving tips and strategies, you may want to view a Video Tutor Solution on [Calculating Angular Velocity](#).
---
#### Part A
**Task:**
Calculate the angular velocity of the merry-go-round as a function of time.
Express your answer in terms of the variables \(\gamma\), \(\beta\), \(t\), and \(\text{rad/s}\).
Input field for equation:
\(\omega(t) = \)
---
#### Part B
**Task:**
What is the initial value of the angular velocity?
Express your answer in radians per second.
Input field for equation:
\(\omega_i = \) \(\text{rad/s}\)
---
#### Part C
**Task:**
Calculate the instantaneous value of the angular velocity \(\omega\) at \(t = 5.40 \, \text{s}\).
Express your answer in radians per second.
Input field for equation:
\(\omega = \) \(\text{rad/s}\)
---
![**Part D**
Calculate the average angular velocity \( \omega_{\text{av\_z}} \) for the time interval \( t = 0 \) to \( t = 5.40 \, \text{s} \).
Express your answer in radians per second.
\[ \omega_{\text{av\_z}} = \] \hspace{3em} \(\text{rad/s}\)
[Submit] [Request Answer]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F76eec8ec-d87c-4fdd-96a3-96e8325f09a2%2F961e0fbb-c36d-4876-9cea-277e3fb721fa%2F3tjgbw_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Part D**
Calculate the average angular velocity \( \omega_{\text{av\_z}} \) for the time interval \( t = 0 \) to \( t = 5.40 \, \text{s} \).
Express your answer in radians per second.
\[ \omega_{\text{av\_z}} = \] \hspace{3em} \(\text{rad/s}\)
[Submit] [Request Answer]
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