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Chapter 4: Problem 66

A car is moving at a rate of 65 miles per hour, and the diameter of its wheels is 2 feet. (a) Find the number of revolutions per minute the wheels are rotating. (b) Find the angular speed of the wheels in radians per minute.

Short Answer

Expert verified
(a) The wheels are rotating at approximately 911.06 revolutions per minute. \n (b) The angular speed of the wheels is 5720 radians per minute.

Step by step solution

01

Conversion of Speed

Convert speed from miles per hour to feet per minute. Knowing that 1 mile equals to 5280 feet and 1 hour equals to 60 minutes, the conversion is as follows: \n Speed = 65 miles/hour * (5280 feet / 1 mile) * (1 hour / 60 minutes) = 5720 feet/minute.
02

Find the Number of Revolutions

Using the formula Circumference = pi * Diameter, the circumference of a wheel is therefore C = 2 * pi feet. The number of revolutions per minute can be calculated by dividing the speed by the circumference of the wheel. Number of revolutions = Speed / C = 5720 / (2 * pi) = 911.06 revolutions/minute.
03

Conversion of Linear Speed to Angular Speed

First, find the radius in feet of each tire (diameter/2 = 1 foot). Then use the formula for angular speed (omega = linear speed / radius) to find the angular speed in radians per minute: Angular speed = Speed / Radius = 5720 / 1 = 5720 rad/minute.

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