A hollow sphere of mass M and radius R = 0.15 m, with rotational inertia I = 0.040 kg · m2 about a line through its center of mass, rolls without slipping up a surface inclinedat θ = 30◦ to the horizontal. At a certain position, say at a height h1 from the ground, thesphere’s total kinetic energy (its center of mass kinetic energy plus its rotational kinetic energy) is 20 J. (Hint: The moment of inertia of such a halo sphere is I = 2/3MR2. Thetranslational speed of a point on the surface of the sphere is the same as the speed of thecenter of mass of the sphere). (a) What ratio of this total kinetic energy is rotational? (b) What is the speed of the center of mass of the sphere at this position? When the sphere has moved d = 1 m up the incline from this (initial) position, using conservation of energy, find (c) its total kinetic energy (d) the speed of its center of mass
A hollow sphere of mass M and radius R = 0.15 m, with rotational inertia I = 0.040 kg · m2 about a line through its center of mass, rolls without slipping up a surface inclinedat θ = 30◦ to the horizontal. At a certain position, say at a height h1 from the ground, thesphere’s total kinetic energy (its center of mass kinetic energy plus its rotational kinetic
energy) is 20 J. (Hint: The moment of inertia of such a halo sphere is I =
2/3MR2. Thetranslational speed of a point on the surface of the sphere is the same as the speed of thecenter of mass of the sphere). (a) What ratio of this total kinetic energy is rotational? (b) What is the speed of the center of mass of the sphere at this position?
When the sphere has moved d = 1 m up the incline from this (initial) position, using conservation of energy, find
(c) its total kinetic energy
(d) the speed of its center of mass
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