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Centripetal Velocity Calculation?

  1. Jan 21, 2016 #1
    I am wondering if someone can show me how to calculate the exit speed of an object if it is dropped into a container which is spinning at 5000 rpm and has a radius of 120mm. Let us assume the object weighs one gram.
    I am building a machine for wear testing. rock/water is supplied to the centre of a spinning rotor and is impacted upon a test specimen, mounted at the exit port.
    Thank you for your time,
    Kevin
     
  2. jcsd
  3. Jan 21, 2016 #2

    mfb

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    This is impossible without many more details about the mechanism. How is the mass dropped into the container, how does it hit the container, how does it leave again, and so on.
    If the container is heavy enough (compared to the dropped object), the speed won't depend on the mass of the object.
     
  4. Jan 22, 2016 #3
    I cannot show the detail due to proprietary reasons but essentially this is what I am describing, a rock dropped into the center of a stainless steel channel, spinning at 5000 RPM;
    https://lh3.googleusercontent.com/9-tYG8bqb8-6z8x6HuCUJBWsmZSGc5vHMBU-mH63KaIWY-6hQFXO-KylOch9CpssdgouIfY60JPtx7JOvGXP4sGKmyUYgohlFAhbg1XVF0bPblQkTkHi7Lg6vl0EHwR3vNcB32VWLhezY-VSRetPP7GtCU5CIAd_pKm6isw1gSbc-CTeGrel3eq-hyYW1dJbzCB5S3lat4NlLaCT8tGNEF4Wyq-E7AkKuU4gyiFgB1Y2uOxUOtrmHo6DlI4crajlM-ZzgNicCiM-7xG2_8kEdaFEMUCz7uYanyiDGNkdgJK-GbbHOzFw0dTMEIr1ew7IYUcpRMcZ1NnJoH4JDLoUQ8EbtZR8T6gzE_mXdtCh-RgSf4-MNwnt5WBLrzdLbOTpv2tWK2pKXD5yBPbiKxSNEp__Bn_rmsMmGrtaT0SHRYRLX24tldTIX5YVQVwSTkSA9sfXQ3CPxcvI_8j-lwYSJrDKCpzyP1GltqN1WDwzc3MO_EgdI8uECouiOkY6n8-KACE9U3cHH6fP-t7BqkiuWk1xnC707hfZcxkVc23cg76_F6Lw3ZSBSrDY1s7EuhhzhKk=w699-h646-no

    Thanks again,
     
  5. Jan 22, 2016 #4

    A.T.

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    The final tangential speed is the speed of the channel ends. The final radial speed will depend on friction in the channel, but ignoring that, you would just integrate the centrifugal acceleration in the rotating frame.
     
  6. Jan 22, 2016 #5

    mfb

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    Ignoring friction, there is an interesting fixed relation between the two speed components.
     
  7. Jan 23, 2016 #6
    Thank you for your insight.
     
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