Math Problem Statement

Do it in rad/minute

Solution

It looks like the previous answer already provided the angular speed in radians per minute, which is 2640.0002640.000 rad/min.

Here's the detailed process for clarity:

Calculation Recap

  1. Speed Conversion: The car's speed is converted from miles per hour to inches per minute. Speed=55mph=55×6336060=58080inches per minute\text{Speed} = 55 \, \text{mph} = \frac{55 \times 63360}{60} = 58080 \, \text{inches per minute}

  2. Wheel Circumference: The wheel's diameter is 44 inches, so its circumference is: C=π×44=138.230inchesC = \pi \times 44 = 138.230 \, \text{inches}

  3. Rotations per Minute: N=58080138.230=420rotations per minuteN = \frac{58080}{138.230} = 420 \, \text{rotations per minute}

  4. Angular Speed: ω=420×2π=2640.000rad/min\omega = 420 \times 2\pi = 2640.000 \, \text{rad/min}

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Math Problem Analysis

Mathematical Concepts

Speed Conversion
Wheel Circumference
Angular Speed

Formulas

Speed conversion formula
Circumference formula
Angular speed formula

Theorems

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Suitable Grade Level

Advanced High School