Problem

A car is being driven on a circular track which has a $300 \mathrm{~m}$ diameter. What is the car's angular velocity, in radians per second, if this car is traveling at $90 \mathrm{~km} / \mathrm{h}$ ?
A) $0.025 \mathrm{rad} / \mathrm{sec}$
C) $0.167 \mathrm{rag} / \mathrm{sec}$
B) $0.083 \mathrm{rad} / \mathrm{sec}$
D) $0.25 \mathrm{rad} / \mathrm{sec}$

Answer

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Answer

\(\boxed{\text{Final Answer: } 0.027 \frac{\text{rad}}{\text{s}}}\) (closest option: A) $0.025 \mathrm{rad} / \mathrm{sec}$)

Steps

Step 1 :Convert the car's speed from km/h to m/s: \(90 \frac{\text{km}}{\text{h}} \times \frac{1000 \text{m}}{1 \text{km}} \times \frac{1 \text{h}}{3600 \text{s}} = 25 \frac{\text{m}}{\text{s}}\)

Step 2 :Find the circumference of the circular track: \(C = \pi d = \pi (300 \text{m}) \approx 942.48 \text{m}\)

Step 3 :Calculate the angular velocity: \(\omega = \frac{\text{speed}}{\text{circumference}} = \frac{25 \frac{\text{m}}{\text{s}}}{942.48 \text{m}} \approx 0.027 \frac{\text{rad}}{\text{s}}\)

Step 4 :\(\boxed{\text{Final Answer: } 0.027 \frac{\text{rad}}{\text{s}}}\) (closest option: A) $0.025 \mathrm{rad} / \mathrm{sec}$)

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