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The radius of the wheel is r=3m. The tangential acceleration is a=2t (m/s2). At t=0, the initial angular position θ0=0 and initial velocity V0=0. After the time of t=6 s, determine

The radius of the wheel is r=3m. The tangential acceleration is a=2t (m/s2). At t=0, the initial angular position θ0=0 and initial velocity V0=0. After the time of t=6 s, determine

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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The radius of the wheel is r=3m. The tangential acceleration is a=2t (m/s2). At t=0, the initial angular position θ0=0 and initial velocity V0=0. After the time of t=6 s, determine

 

(3) the angular position, θ= _________ rad (round to 3 desimal places)




### Problem Statement The radius of the wheel is \( r = 3 \, \text{m} \). The tangential acceleration is \( a = 2t \left( \frac{m}{s^2} \right) \). At \( t = 0 \), the initial angular position \( \theta_0 = 0 \) and initial velocity \( V_0 = 0 \). After a time of \( t = 6 \, \text{s} \), determine: (3) The angular position, \( \theta = \_\_\_\_\_\_\_\_\_\_ \) rad (round to 3 decimal places). ### Diagram Explanation The accompanying diagram illustrates a wheel with a radius \( r \). - The wheel is oriented with a point on its circumference labeled \( A \). - The tangential acceleration is shown as \( a_t \) in a direction tangent to the circumference at point \( A \). - The centripetal acceleration is shown towards the center of the wheel, denoted as \( a_c \). - The diagram emphasizes the angular position and the radius \( r \) of the wheel. This setup provides the basis for solving the problem of determining the angular position after a given time period with specified initial conditions and a time-varying tangential acceleration.
Transcribed Image Text:### Problem Statement The radius of the wheel is \( r = 3 \, \text{m} \). The tangential acceleration is \( a = 2t \left( \frac{m}{s^2} \right) \). At \( t = 0 \), the initial angular position \( \theta_0 = 0 \) and initial velocity \( V_0 = 0 \). After a time of \( t = 6 \, \text{s} \), determine: (3) The angular position, \( \theta = \_\_\_\_\_\_\_\_\_\_ \) rad (round to 3 decimal places). ### Diagram Explanation The accompanying diagram illustrates a wheel with a radius \( r \). - The wheel is oriented with a point on its circumference labeled \( A \). - The tangential acceleration is shown as \( a_t \) in a direction tangent to the circumference at point \( A \). - The centripetal acceleration is shown towards the center of the wheel, denoted as \( a_c \). - The diagram emphasizes the angular position and the radius \( r \) of the wheel. This setup provides the basis for solving the problem of determining the angular position after a given time period with specified initial conditions and a time-varying tangential acceleration.
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