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Math Help - Circular Motion

  1. #1
    pre-agitated
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    Circular Motion

    An object is traveling around a circle with the radius of 5cm. If in 20sec the central angle of 1/3 radian is swept out, what is the angular speed of the object? Linear speed?

    Here's how I did it. angular speed-->
    a) omega=theta(in radians)/elapsed time
    = π/3/20= π/3*1/20 = π/60 radians/sec. Is that the same as the answer in the book, 1/60?

    linear speed-->
    b) v=rw (length/radius)(omega=angular speed)
    =5cm*(1/60)= 1/12 cm/s
    the answer in the book is 12m/s.

    what did I do wrong?
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by pre-agitated View Post
    An object is traveling around a circle with the radius of 5cm. If in 20sec the central angle of 1/3 radian is swept out, what is the angular speed of the object? Linear speed?

    Here's how I did it. angular speed-->
    a) omega=theta(in radians)/elapsed time
    = π/3/20= π/3*1/20 = π/60 radians/sec. Is that the same as the answer in the book, 1/60?

    linear speed-->
    b) v=rw (length/radius)(omega=angular speed)
    =5cm*(1/60)= 1/12 cm/s
    the answer in the book is 12m/s.

    what did I do wrong?
    a) An angle of \frac{1}{3} rad is, like, \frac{1}{3} rad. Why are you sticking the \pi in there? That's your only mistake.

    b) Looks like you are correct and the book is wrong. Always such fun when that happens!

    -Dan
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