a ferris wheel rotates through an angle of $\frac{7\pi}{6}$ radians in 45 seconds.

how many degrees will it rotate through in 5 minutes?

Question

a ferris wheel rotates through an angle of $\frac{7\pi}{6}$ radians in 45 seconds.

how many degrees will it rotate through in 5 minutes?

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Radian to Degree Conversion" ], "new_concepts": [ "Angular Speed Word Problems" ], "current_concepts": [ "Radian to Degree Conversion", "Angular Speed Word Problems" ] } ## Convert the rotation angle to degrees $$ \theta = \frac{7\pi}{6} \times \frac{180^\circ}{\pi} = 210^\circ $$ ## Calculate the rotation rate in degrees per second $$ \omega = \frac{210^\circ}{45\text{ s}} = \frac{14}{3}^\circ/\text{s} $$ ## Calculate the total rotation in 5 minutes $$ \begin{aligned} t &= 5 \times 60\text{ s} = 300\text{ s} \ \theta_{\text{total}} &= \frac{14}{3}^\circ/\text{s} \times 300\text{ s} = 1400^\circ \end{aligned} $$ $1400^\circ$ { "subject": "Mathematics", "question_type": "Word Problem", "knowledge_point": [ "Mathematics", "Geometry", "Radian to Degree Conversion" ] }

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QUESTION IMAGE

Question

Explanation:

Convert the rotation angle to degrees

Calculate the rotation rate in degrees per second

Calculate the total rotation in 5 minutes

Answer: