Discover answers to your most pressing questions at Westonci.ca, the ultimate Q&A platform that connects you with expert solutions. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.
Sagot :
To determine the angular displacement of a figure skater who starts from rest and accelerates with a constant acceleration of 100 °/s² over a time period of 1 second, we can use the kinematic equation for rotational motion:
[tex]\[ \theta = \omega_0 t + \frac{1}{2} \alpha t^2 \][/tex]
where:
- [tex]\(\theta\)[/tex] is the angular displacement.
- [tex]\(\omega_0\)[/tex] is the initial angular velocity.
- [tex]\(\alpha\)[/tex] is the angular acceleration.
- [tex]\(t\)[/tex] is the time.
Given the problem parameters:
- The skater starts from rest, so the initial angular velocity [tex]\(\omega_0\)[/tex] is 0 °/s.
- The angular acceleration [tex]\(\alpha\)[/tex] is 100 °/s².
- The time [tex]\(t\)[/tex] is 1 second.
Plugging in these values:
[tex]\[ \theta = 0 \cdot 1 + \frac{1}{2} \cdot 100 \cdot 1^2 \][/tex]
[tex]\[ \theta = 0 + \frac{1}{2} \cdot 100 \cdot 1 \][/tex]
[tex]\[ \theta = \frac{100}{2} \][/tex]
[tex]\[ \theta = 50 \text{ degrees} \][/tex]
Thus, the angular displacement over 1 second is [tex]\(50^\circ\)[/tex].
Therefore, the correct answer is:
50°
[tex]\[ \theta = \omega_0 t + \frac{1}{2} \alpha t^2 \][/tex]
where:
- [tex]\(\theta\)[/tex] is the angular displacement.
- [tex]\(\omega_0\)[/tex] is the initial angular velocity.
- [tex]\(\alpha\)[/tex] is the angular acceleration.
- [tex]\(t\)[/tex] is the time.
Given the problem parameters:
- The skater starts from rest, so the initial angular velocity [tex]\(\omega_0\)[/tex] is 0 °/s.
- The angular acceleration [tex]\(\alpha\)[/tex] is 100 °/s².
- The time [tex]\(t\)[/tex] is 1 second.
Plugging in these values:
[tex]\[ \theta = 0 \cdot 1 + \frac{1}{2} \cdot 100 \cdot 1^2 \][/tex]
[tex]\[ \theta = 0 + \frac{1}{2} \cdot 100 \cdot 1 \][/tex]
[tex]\[ \theta = \frac{100}{2} \][/tex]
[tex]\[ \theta = 50 \text{ degrees} \][/tex]
Thus, the angular displacement over 1 second is [tex]\(50^\circ\)[/tex].
Therefore, the correct answer is:
50°
Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.