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Math Help - Angular and Linear Speed.

  1. #1
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    Angular and Linear Speed.

    My prof posted this problem as an example and, going over the steps, I haven't been able to work out how he got to the final answer.

    A car has tires with 10 inch radius and is traveling at 60 miles per hour. Find the angular speed of the wheels in radians per second.

    (60 miles/hr) = (60 miles/hr) * (5280 ft/1 mile) * (12 in/1 ft) * (2 pi rad/2 pi (10 in)) * (60 min/1 in) * (60 sec/1 min)

    = 1.4*10^9 rad/sec

    I'm not totally sure how he got to that final answer. When I tried it, I got something completely different. I'd appreciate a hint to the right direction.
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: Angular and Linear Speed.

    The angular speed \omega is given as a function of the linear speed v and radius r as:

    \omega=\frac{v}{r}

    To find \omega in radians per second, given that r is in inches, we need to convert v to inches per second:

    \omega=\frac{60\frac{\text{mi}}{\text{hr}}\cdot \frac{5280\text{ ft}}{1\text{ mi}}\cdot \frac{12\text{ in}}{1\text{ ft}}\cdot \frac{1\text{ hr}}{3600\text{ s}}}{10\text{ in}}=105.6\,\frac{\text{rad}}{\text{ s}}
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