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A coin rests 15 cm away from the center of a turntable. The turntable starts to rotate at an angular acceleration of .8 rad/s^2 and after 7 seconds it slides off. What is the coefficient of static friction between the coin and the surface?

Just give me step by step on how to solve this problem.

  • physics -

    It starts sliding when the static friction force reaches its maximum value. Its maximum value is Us*M*g.
    Us is the static coefficeint you want to determine

    After 7 seconds, the angular velocity is 5.6 rad/s and the centripetal acceleration is
    Rw^2 = -.15*(5.6)^2 = 4.7 m/s^2.
    There is also continuing tangential acceleration of R*alpha = 0.12 m/s^2 The vector-sum acceleration is
    4.701 m/s^2, so you can ignore the tangential acceleration effect.

    Us*M*g = M R w^2
    Us = R w^2/g = 4.7/9.8 = 0.48

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