after fixing a flat tire on a bicycle you give the wheel a spin. its initial angular speed was $7.00\text{ rad/s}$ and it rotated $12.8\text{ revolutions}$ before coming to rest.

part a
what was its average angular acceleration?
express your answer using three significant figures.
$\alpha = $ $\text{rad/s}^2$

part b
for what length of time did the wheel rotate?
express your answer using three significant figures.
$t = $ $\text{s}$

Question

after fixing a flat tire on a bicycle you give the wheel a spin. its initial angular speed was $7.00\text{ rad/s}$ and it rotated $12.8\text{ revolutions}$ before coming to rest.

part a
what was its average angular acceleration?
express your answer using three significant figures.
$\alpha = $ $\text{rad/s}^2$

part b
for what length of time did the wheel rotate?
express your answer using three significant figures.
$t = $ $\text{s}$

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Rotational Kinematics" ], "new_concepts": [], "current_concepts": [ "Rotational Kinematics" ] } ## Calculate average angular acceleration $$ \begin{aligned} \omega_0 &= 7.00\text{ rad/s} \ \omega_f &= 0\text{ rad/s} \ \theta &= 12.8\text{ rev} \times 2\pi\text{ rad/rev} = 25.6\pi\text{ rad} \approx 80.425\text{ rad} \ \omega_f^2 &= \omega_0^2 + 2\alpha\theta \ 0^2 &= (7.00)^2 + 2\alpha(25.6\pi) \ \alpha &= -\frac{49.0}{51.2\pi} \approx -0.3046\text{ rad/s}^2 \approx -0.305\text{ rad/s}^2 \end{aligned} $$ ## Calculate rotation time $$ \begin{aligned} \theta &= \frac{\omega_0 + \omega_f}{2} t \ 25.6\pi &= \frac{7.00 + 0}{2} t \ t &= \frac{51.2\pi}{7.00} \approx 22.978\text{ s} \approx 23.0\text{ s} \end{aligned} $$ ## Question 1 $\alpha = -0.305$ ## Question 2 $t = 23.0$ { "subject": "Natural Science", "question_type": "Multi-part", "knowledge_point": [ "Natural Science", "Physics", "Rotational Kinematics" ] }

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QUESTION IMAGE

Question

Explanation:

Calculate average angular acceleration

Calculate rotation time

Answer:

Question 1

Question 2