Answered

Find the best answers to your questions at Westonci.ca, where experts and enthusiasts provide accurate, reliable information. Get immediate answers to your questions from a wide network of experienced professionals on our Q&A platform. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.

A car speeds up uniformly while rounding a turn. The car's angular speed increases from 0.54 radians per second to 0.96 radians per second as it turns through 1.40 radians. What is the car's angular acceleration? Include units in your answer. Answer must be in 3 significant digits.

Sagot :

Given data:

* The initial angular speed of the car is,

[tex]\omega_i=0.54\text{ rad/s}[/tex]

* The final angular speed of the car is,

[tex]\omega_f=0.96\text{ rad/s}[/tex]

* The angular displacement of the car is,

[tex]\theta=1.4\text{ radians}[/tex]

Solution:

By the kinematics equation, the angular acceleration of the car in terms of the angular displacement is,

[tex]\omega^2_{\text{f}}-\omega^2_i=2\alpha\theta[/tex]

where,

[tex]\alpha\text{ is the angular acceleration,}[/tex]

Substituting the known values,

[tex]\begin{gathered} 0.96^2-0.54^2=2\times\alpha\times1.4 \\ \alpha=\frac{0.96^2-0.54^2}{2\times1.4} \\ \alpha=\frac{0.9216-0.2916}{2.8} \\ \alpha=\frac{0.63}{2.8} \end{gathered}[/tex]

By simplifying,

[tex]\alpha=0.225rads^{-2}[/tex]

Thus, the angular acceleration of the car is 0.225 radians per second squared.

Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.