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Math Help - Angular velocity

  1. #1
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    Unhappy Angular velocity

    A car tire has diameter 64 cm. Determine its angular velocity, in radians per second, when the car is traveling at 100 km/h.

    So I want to find the number of rotations the tire makes in one second, and to do that I divide the velocity of the car by the circumference of the tire. (I think)
    100 km/h = 27.78 m/s

    \pi 64=201.06 cm = .201 m is the circumference of the circle in meters.


    \frac{27.78}{.201}=138.5 is the number of rotations per second.

    So the circle makes approximately 138.5 rotations per second. I know that an entire circle is 2\pi radians so I just multiple 138.5 by 2\pi and that works out to be 870.22 radians/s.

    The answer is supposed to be 86.83 radians/s and I don't know what I'm doing wrong. Could someone please explain?

    Write an expression for the angular velocity, in radians per second, for a car tire with diameter d centimeters when the car is traveling at x kilometers per hour.
    I have no idea how to start this one. Help!


    Last edited by iamanoobatmath; July 4th 2009 at 01:12 PM.
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  2. #2
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    angular speed, \omega = \frac{v}{r}

    v = 100 km/hr = \frac{250}{9} m/s

    r = 32 cm = .32 m

    \frac{v}{r} \approx 86.8 rad/s
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  3. #3
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    Quote Originally Posted by iamanoobatmath View Post
    So I want to find the number of rotations the tire makes in one second, and to do that I divide the velocity of the car by the circumference of the tire. (I think)
    100 km/h = 27.78 m/s

    \pi 64=201.06 cm = .201 m is the circumference of the circle in meters.


    \frac{27.78}{.201}=138.5 is the number of rotations per second.

    So the circle makes approximately 138.5 rotations per second. I know that an entire circle is 2\pi radians so I just multiple 138.5 by 2\pi and that works out to be 870.22 radians/s.

    The answer is supposed to be 86.83 radians/s and I don't know what I'm doing wrong. Could someone please explain?



    I have no idea how to start this one. Help!



    \pi 64=201.06 cm = .201 m is the circumference of the circle in meters.

    check your conversion: 201.06 cm = 2.01 m

    Looks as if you have it.
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  4. #4
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    Quote Originally Posted by iamanoobatmath View Post
    A car tire has diameter 64 cm. Determine its angular velocity, in radians per second, when the car is traveling at 100 km/h.
    An alternative (but longer) method would be to make a series of multiplications of different unit ratios, from km/h to rad/s, like this:
    \left(\frac{100 km}{1 hr}\right)\left(\frac{1,000 m}{1 km}\right)\left(\frac{100 cm}{1 m}\right)\left(\frac{1 rad}{32 cm}\right)\left(\frac{1 hr}{60 min}\right)\left(\frac{1 min}{60 sec}\right).

    That way, when multiplying out, all of the units cancel except for radians on top and seconds on bottom. I get ~86.81 rad/s as my answer.


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