A solid sphere of radius 16.0 cm and mass 10.0 kg starts from rest and rolls wit

Question

A solid sphere of radius 16.0 cm and mass 10.0 kg starts from rest and rolls without slipping a distance of L = 6.0 m down a house roof that is inclined at 39

A solid sphere of radius 16.0 cm and mass 10.0 kg starts from rest and rolls without slipping a distance of L = 6.0 m down a house roof that is inclined at 39degree. The height of the outside wall of the house is h = 9 m. What is the angular speed about its center as it leaves the house roof? What is the horizontal displacement of the sphere between the time it which it leaves the roof and the time at which it hits the ground?

Explanation / Answer

(a)
(initial gravitational potential energy) = (final translational kinetic energy) + (final rotational kinetic energy)
mgLsin? = mv^2/2 + I?^2/2

moment of inertia of solid cylinder: I = mr^2/2

mgLsin? = m(?r)^2/2 + (mr^2/2)(?^2/2)
gLsin? = 3(?r)^2/4
sqrt{4gLsin?/3} / r = ?
? = sqrt{4(9.81 m/s^2)(6.0 m)(sin(39

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