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30 April, 14:57

Certain neutron stars (extremely dense stars) are believed to be rotating at about 1 rev/s. If such a star has a radius of 20 km, what must be its minimum mass so that material on its surface remains in place during the rapid rotation? Hint: The equator of the star is where the maximum centripetal acceleration occurs.

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  1. 30 April, 18:08
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    M = 4.7 10²⁴ kg

    Explanation:

    For this exercise we must use the law of universal gravitation

    F = G m M / r²

    Newton's second law with centripetal acceleration

    a = v² / r

    v = w r

    a = w² r

    F = m a

    G m M / r2 = m w2 r

    G M = w² r³

    M = w² r³ / G

    Let's reduce the magnitudes to the SI system

    w = 1 rev / s (2π rad / 1 rev) = 2π rad / s

    r = 20 km (1000m / 1 km) = 2 10⁴ m

    Let's calculate

    M = (2π) ²2 (2 10⁴) ³ / 6.67 10⁻¹¹

    M = 47.35 10²³ kg

    M = 4.7 10²⁴ kg
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