a spot of paint on a bicycle tire moves in a circular path of radius $0.29\text{ m}$.

part a
when the spot has traveled a linear distance of $2.64\text{ m}$, through what angle has the tire rotated? give your answer in radians.
express your answer using two significant figures.
$\phi = $ $\text{rad}$

Question

a spot of paint on a bicycle tire moves in a circular path of radius $0.29\text{ m}$.

part a
when the spot has traveled a linear distance of $2.64\text{ m}$, through what angle has the tire rotated? give your answer in radians.
express your answer using two significant figures.
$\phi = $   $\text{rad}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Rotational Kinematics" ], "new_concepts": [], "current_concepts": [ "Rotational Kinematics", "Arc Length" ] } ## Relate arc length to angular displacement $$ s = r\theta \implies \theta = \frac{s}{r} $$ ## Substitute given values $$ \begin{aligned} s &= 2.64\text{ m} \ r &= 0.29\text{ m} \ \theta &= \frac{2.64}{0.29} \approx 9.1034\text{ rad} \end{aligned} $$ ## Round to two significant figures $$ \phi = 9.1\text{ rad} $$ When the spot has traveled a linear distance of 2.64 m, through what angle has the tire rotated? Give your answer in radians. Express your answer using two significant figures. $\phi =$ 9.1 rad { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Arc Length" ] }

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Question

Explanation:

Relate arc length to angular displacement

Substitute given values

Round to two significant figures

Answer: