A cylinder with its mass concentrated toward the center has a moment of inertia of 0.1 MR².If this cylinder is rolling without slipping along a level surface with a linear speed v,what is the ratio of its rotational kinetic energy to its linear kinetic energy? A)1/l0 B)1/5 C)1/2 D)1/1

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Quizplus · Accepted Answer

The rotational kinetic energy of a cylinder is given by (1/2)Iω^2, where I is the moment of inertia and ω is the angular velocity. The linear kinetic energy of a cylinder is given by (1/2)Mv^2, where M is the mass and v is the linear velocity. The angular velocity is related to the linear velocity by ω = v/R, where R is the radius of the cylinder. Substituting this into the equation for rotational kinetic energy, we get (1/2)I(v/R)^2 = (1/2)(0.1 MR^2)(v^2/R^2) = (1/20)Mv^2. Therefore, the ratio of rotational kinetic energy to linear kinetic energy is (1/20)Mv^2/(1/2)Mv^2 = 1/10.

A Cylinder with Its Mass Concentrated Toward the Center Has