Part C Calculate the instantaneous value of the angular velocity wz at t= 5.05 s. 1D ΑΣΦ www ? rad/s Request Answer Part D Calculate the average angular velocity wav for the time interval t=0 to £= 5.05 s. VD ΑΣΦ ? Way = rad/s Submit Request Answer لیا Submit
Part C Calculate the instantaneous value of the angular velocity wz at t= 5.05 s. 1D ΑΣΦ www ? rad/s Request Answer Part D Calculate the average angular velocity wav for the time interval t=0 to £= 5.05 s. VD ΑΣΦ ? Way = rad/s Submit Request Answer لیا Submit
Part C Calculate the instantaneous value of the angular velocity wz at t= 5.05 s. 1D ΑΣΦ www ? rad/s Request Answer Part D Calculate the average angular velocity wav for the time interval t=0 to £= 5.05 s. VD ΑΣΦ ? Way = rad/s Submit Request Answer لیا Submit
1. Calculate the angular velocity of the merry-go-round as a function of time.
Express your answer in terms of the variables β, γ, and t.
2. What is the initial value of the angular velocity?
other 2 questions are attached
Transcribed Image Text:### Part C
#### Calculate the instantaneous value of the angular velocity \(\omega_z\) at \( t = 5.05 \, \text{s} \).
##### Input Box
\[ \omega_z = \quad \quad \quad \quad \quad \quad \quad \text{rad/s} \]
**Buttons Available for Input:**
- **Graph (Function) Tool**: Allows for graphing functions and equations.
- **Equation Tool**: Insertion of mathematical equations.
- **Undo/Redo Buttons**: To undo or redo recent changes.
- **Statistics Tool**: For statistical calculations.
- **Greek Symbols Tool**: For inserting Greek letters.
- **Reset Button**: Clears the entered data.
- **Constants Button**: For inserting physical constants.
- **Help Button**: Provides additional help.
**Action Buttons:**
- **Submit**: Submits your calculated answer.
- **Request Answer**: Requests the correct answer.
### Part D
#### Calculate the average angular velocity \(\omega_{\text{av}_z}\) for the time interval \( t = 0 \) to \( t = 5.05 \, \text{s} \).
##### Input Box
\[ \omega_{\text{av}_z} = \quad \quad \quad \quad \quad \quad \quad \text{rad/s} \]
**Buttons Available for Input:**
- **Graph (Function) Tool**: Allows for graphing functions and equations.
- **Equation Tool**: Insertion of mathematical equations.
- **Undo/Redo Buttons**: To undo or redo recent changes.
- **Statistics Tool**: For statistical calculations.
- **Greek Symbols Tool**: For inserting Greek letters.
- **Reset Button**: Clears the entered data.
- **Constants Button**: For inserting physical constants.
- **Help Button**: Provides additional help.
**Action Buttons:**
- **Submit**: Submits your calculated answer.
- **Request Answer**: Requests the correct answer.
Transcribed Image Text:**Angular Motion of a Merry-Go-Round**
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:
- \(\gamma = 0.406 \, \text{rad/s}\)
- \(\beta = 1.30 \times 10^{-2} \, \text{rad/s}^3\)
In this equation:
- \(\theta(t)\) represents the angle in radians through which the merry-go-round has turned after time \(t\).
- \(\gamma\) is a constant representing the angular velocity component in radians per second.
- \(\beta\) is a constant representing the angular acceleration component that influences the cubic term of time in the equation.
This mathematical model helps to describe the rotational motion of the merry-go-round over time.
Definition Definition Rate of change of angular displacement. Angular velocity indicates how fast an object is rotating. It is a vector quantity and has both magnitude and direction. The magnitude of angular velocity is represented by the length of the vector and the direction of angular velocity is represented by the right-hand thumb rule. It is generally represented by ω.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
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.
![### Part C
#### Calculate the instantaneous value of the angular velocity \(\omega_z\) at \( t = 5.05 \, \text{s} \).
##### Input Box
\[ \omega_z = \quad \quad \quad \quad \quad \quad \quad \text{rad/s} \]
**Buttons Available for Input:**
- **Graph (Function) Tool**: Allows for graphing functions and equations.
- **Equation Tool**: Insertion of mathematical equations.
- **Undo/Redo Buttons**: To undo or redo recent changes.
- **Statistics Tool**: For statistical calculations.
- **Greek Symbols Tool**: For inserting Greek letters.
- **Reset Button**: Clears the entered data.
- **Constants Button**: For inserting physical constants.
- **Help Button**: Provides additional help.
**Action Buttons:**
- **Submit**: Submits your calculated answer.
- **Request Answer**: Requests the correct answer.
### Part D
#### Calculate the average angular velocity \(\omega_{\text{av}_z}\) for the time interval \( t = 0 \) to \( t = 5.05 \, \text{s} \).
##### Input Box
\[ \omega_{\text{av}_z} = \quad \quad \quad \quad \quad \quad \quad \text{rad/s} \]
**Buttons Available for Input:**
- **Graph (Function) Tool**: Allows for graphing functions and equations.
- **Equation Tool**: Insertion of mathematical equations.
- **Undo/Redo Buttons**: To undo or redo recent changes.
- **Statistics Tool**: For statistical calculations.
- **Greek Symbols Tool**: For inserting Greek letters.
- **Reset Button**: Clears the entered data.
- **Constants Button**: For inserting physical constants.
- **Help Button**: Provides additional help.
**Action Buttons:**
- **Submit**: Submits your calculated answer.
- **Request Answer**: Requests the correct answer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fddf14729-dbf2-4574-b793-bebd8df9c378%2Febdb9105-2c68-4888-b560-8a81ba73fbd9%2Fdr01znq_processed.png&w=3840&q=75)
![**Angular Motion of a Merry-Go-Round**
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:
- \(\gamma = 0.406 \, \text{rad/s}\)
- \(\beta = 1.30 \times 10^{-2} \, \text{rad/s}^3\)
In this equation:
- \(\theta(t)\) represents the angle in radians through which the merry-go-round has turned after time \(t\).
- \(\gamma\) is a constant representing the angular velocity component in radians per second.
- \(\beta\) is a constant representing the angular acceleration component that influences the cubic term of time in the equation.
This mathematical model helps to describe the rotational motion of the merry-go-round over time.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fddf14729-dbf2-4574-b793-bebd8df9c378%2Febdb9105-2c68-4888-b560-8a81ba73fbd9%2F6viat1d_processed.png&w=3840&q=75)
