Two hoops, starting from rest, roll down identical inclined planes. The work done by nonconservative forces, such as air resiste
nce, is zero (Wnc = 0J). Both have the same mass M, but, one hoop has the twice the radius of the other. The moment of inertia for each hoop is I = Mr sequared, where r is the radius. Which hoop, if either has the greater total kinetic energy (transational and rotational) at the bottom of the incline. Hoop 1 Radius = R and Mass = M
Hoop 2 Radius = 1/2 R and Mass = M
Kepler’s three law is the answer. Kepler’s 3 is the amount
of time it takes to orbit the sun is related to size and distance. Kepler’s 3 is one of the planetary motion and
can be stated as all planets move in elliptical orbits, having the sun sits at
one of the foci.
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