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Math Help - i need help w/ linear/angular speed

  1. #1
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    i need help w/ linear/angular speed

    An object is traveling around a circle with a radius of 10 cm. If in 20s a central angle of 1/3 radians is swept out, what is the linear speed of the object?
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by tangerine_tomato View Post
    An object is traveling around a circle with a radius of 10 cm. If in 20s a central angle of 1/3 radians is swept out, what is the linear speed of the object?
    You can do this in two ways.
    1. v = d / t
    The distance traveled is the arc length swept out. So d = (10 cm)(1/3 rad) = 10/3 cm. This is covered in 20 s, so
    v = \frac{d}{t} = \frac{\frac{10}{3}~cm}{20~s} = \frac{1}{6}~cm/s

    2. Find the angular speed from omega = \theta / t then find the linear speed by v = r \omega. It comes out to be the same thing in the end.

    -Dan
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    Quote Originally Posted by topsquark View Post
    You can do this in two ways.
    1. v = d / t
    The distance traveled is the arc length swept out. So d = (10 cm)(1/3 rad) = 10/3 cm. This is covered in 20 s, so
    v = \frac{d}{t} = \frac{\frac{10}{3}~cm}{20~s} = \frac{1}{6}~cm/s

    2. Find the angular speed from omega = \theta / t then find the linear speed by v = r \omega. It comes out to be the same thing in the end.

    -Dan
    i dont understand how you find 10/3 for D
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  4. #4
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by tangerine_tomato View Post
    i dont understand how you find 10/3 for D
    The arc length s (I used "d" here) is defined by s = r \theta where \theta is the central angle measured in radians.

    -Dan
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