A hoop with mass,M,and radius,R,rolls along a level surface without slipping with a linear speed,v.What is the ratio of rotational to linear kinetic energy? (For a hoop,I = MR². ) A)1/4 B)1/2 C)1/1 D)2/5

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Quizplus · Accepted Answer

The rotational kinetic energy (K_rot) for a hoop is given by (1/2)Iω^2, where I is the moment of inertia and ω is the angular velocity. For a hoop, I = MR^2. The linear kinetic energy (K_lin) is given by (1/2)Mv^2. Since the hoop rolls without slipping, v = ωR. Substituting ω = v/R into the rotational kinetic energy formula gives (1/2)MR^2(v/R)^2 = (1/2)Mv^2, which is equal to the linear kinetic energy. Therefore, the ratio of rotational to linear kinetic energy is 1:1.

A Hoop with Mass,M,and Radius,R,rolls Along a Level Surface Without