the moment of inertia of a $1.2\text{ kg}$ bicycle wheel rotating about its center is $0.12\text{ kg}\cdot\text{m}^2$.

part a
what is the radius of this wheel, assuming the weight of the spokes can be ignored?
express your answer with the appropriate units.

Question

the moment of inertia of a $1.2\text{ kg}$ bicycle wheel rotating about its center is $0.12\text{ kg}\cdot\text{m}^2$.

part a
what is the radius of this wheel, assuming the weight of the spokes can be ignored?
express your answer with the appropriate units.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Moment of Inertia" ], "new_concepts": [ "Rotational Inertia of a Thin Ring" ], "current_concepts": [ "Moment of Inertia", "Rotational Inertia of a Thin Ring" ] } ## Identify the given parameters and formula for a thin ring $$ \begin{aligned} &m = 1.2\text{ kg}\ &I = 0.12\text{ kg}\cdot\text{m}^2\ &I = mR^2 \end{aligned} $$ ## Solve for the radius $R$ $$ \begin{aligned} &R^2 = \frac{I}{m} = \frac{0.12\text{ kg}\cdot\text{m}^2}{1.2\text{ kg}} = 0.1\text{ m}^2\ &R = \sqrt{0.1\text{ m}^2} \approx 0.3162\text{ m} \end{aligned} $$ ## Round to two significant figures $$ R \approx 0.32\text{ m} $$ What is the radius of this wheel, assuming the weight of the spokes can be ignored? $R =$ $0.32\text{ m}$ { "subject": "Natural Science", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Natural Science", "Physics", "Rotational Inertia" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the given parameters and formula for a thin ring

Solve for the radius \(R\)

Round to two significant figures

Answer: