a soccer ball, which has a circumference of 70.0 cm, rolls 12.5 yards in 3.55 s.

part a
what was the average angular speed of the ball during this time?
\omega = \text{ rad/s}

Question

a soccer ball, which has a circumference of 70.0 cm, rolls 12.5 yards in 3.55 s.

part a
what was the average angular speed of the ball during this time?
\omega = \text{ rad/s}

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Unit Conversion", "Rotational Kinematics" ], "new_concepts": [ "Rolling Motion Relations" ], "current_concepts": [ "Unit Conversion", "Rotational Kinematics", "Rolling Motion Relations" ] } ## Convert given values to standard SI units $$ \begin{aligned} C &= 70.0\text{ cm} = 0.700\text{ m} \ d &= 12.5\text{ yd} = 12.5 \times 0.9144\text{ m} = 11.43\text{ m} \ t &= 3.55\text{ s} \end{aligned} $$ ## Calculate average linear speed $$ v = \frac{d}{t} = \frac{11.43\text{ m}}{3.55\text{ s}} \approx 3.2197\text{ m/s} $$ ## Calculate average angular speed $$ \begin{aligned} R &= \frac{C}{2\pi} = \frac{0.700\text{ m}}{2\pi} \approx 0.1114\text{ m} \ \omega &= \frac{v}{R} = \frac{3.2197\text{ m/s}}{0.1114\text{ m}} \approx 28.9\text{ rad/s} \end{aligned} $$ What was the average angular speed of the ball during this time? $\omega =$ $28.9$ $\text{rad/s}$ { "subject": "Natural Science", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Natural Science", "Physics", "Rotational Kinematics" ] }

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Question

Explanation:

Convert given values to standard SI units

Calculate average linear speed

Calculate average angular speed

Answer: