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25 May, 09:28

A solid cylinder of radius 10 cm and mass 12 kg starts from rest and rolls without slipping a distance L = 6.0 m down a roof that is inclined at the angle theta = 30degree.

(a) What is the angular speed of the cylinder about its center as it leaves the roof?

(b) The roofs edge is at height H = 5.0 m. How far horizontally from the roof's edge does the cylinder hit the level ground?

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  1. 25 May, 09:46
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    Acceleration of cylinder

    a = g sin 30 / 1 + k² / r² where k is radius of gyration and r is radius of cylinder.

    For cylinder k² = (1 / 2) r²

    acceleration

    = gsin30 / 1.5

    = g / 3

    = 3.27

    v² = u² + 2as

    = 2 x 3.27 x 6

    v = 6.26 m / s

    v = angular velocity x radius

    6.26 = angular velocity x. 10

    angular velocity = 62.6 rad / s

    b) vertical component of velocity

    = 6.26 sin 30

    = 3.13 m / s

    h = ut + 1/2 g t²

    5 = 3.13 t +.5 t²

    .5 t² + 3.13 t - 5 = 0

    t = 1.32 s

    horizontal distance covered

    = 6.26 cos 30 x 1.32

    = 7.15 m
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