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Math Help - Linear and Angular Velocity

  1. #1
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    Linear and Angular Velocity

    On rewinding a VHS tape, the takeup spool rotates at 540 rpm. Find the speed of the tape in meters per minute and the angular velocity of the other spool when the takeup spool has a 20-mm thickness of tape on its 10-mm radius and the other spool has a 10-mm thickness of tape on it.
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  2. #2
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    Re: Linear and Angular Velocity

    In order to do this you should also know the thickness of the tape. With each rotation, one "layer" of tape is added to the take up real and removed from the other reel so their radii, and so circumferences, the length of tape that comes off, will change.
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  3. #3
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    Re: Linear and Angular Velocity

    The radius of the takeup spool is 10 mm, and the thickness of the tape on it is 20 mm. Does this mean, I have to calculate the radius as 30 mm?
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  4. #4
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    Re: Linear and Angular Velocity

    No, not "the thickness of the tape on it" is NOT the thickness of the tape itself. It is the thickness of whatever number of layers of tape are on the spool. The initial radius is 30 mm but that changes with each rotation.
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  5. #5
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    Re: Linear and Angular Velocity

    If the formula says

    v = rw

    Is it correct to plug

    v = 30 mm (540 r/min)

    to find the speed of the tape?
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