We have a wagonwheel ready to roll without slipping from a height “h.” The radius of the wagonwheel is “r” and it is made of a thin hoop and 8 spokes symmetrically arranged all meeting at the center of mass which is the center of the hoop and ending at the hoop itself. The hoop and each individual spoke all have equal mass. When it is released from rest, it will roll without slipping toward the loop-the-loop. The loop-the-loop has a radius “R.” The wagonwheel sidesteps the loop-the-loop at first with a negligible offset in the z-direction in order to enter it. You may assume that the wagonwheel radius “r” is much much less than “R” so that the point of contact of the wagonwheel can be treated as if it is in the center-of-mass location of the wheel for brevity. What is the composite moment of inertia of the wagonwheel? Express your answer algebraically. What is the velocity of the wagonwheel at the top of the loop if it is locked to the path and therefore not allowed to fall off? Suppose the height “h” of release is 25 meters and the radius “R” of the loop-the-loop is 10 meters. If the wagonwheel is unlocked and is now allowed to fall off, will it fall off the loop-the-loop and crash before reaching the top? A specific value for the radius “r” of the wagonwheel is not needed, nor is the wagonwheel’s mass.

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We have a wagonwheel ready to roll without slipping from a height “h.” The radius of the wagonwheel is “r” and it is made of a thin hoop and 8 spokes symmetrically arranged all meeting at the center of mass which is the center of the hoop and ending at the hoop itself. The hoop and each individual spoke all have equal mass. When it is released from rest, it will roll

without slipping toward the loop-the-loop. The loop-the-loop has a radius “R.” The wagonwheel sidesteps the loop-the-loop at first with a negligible offset in the z-direction in order to enter it. You may assume that the wagonwheel radius “r” is much much less than “R” so that the point of contact of the wagonwheel can be treated as if it is in the center-of-mass location of the wheel for brevity.

What is the composite moment of inertia of the wagonwheel? Express your answer algebraically.

What is the velocity of the wagonwheel at the top of the loop if it is locked to the path and therefore not allowed to fall off?

Suppose the height “h” of release is 25 meters and the radius “R” of the loop-the-loop is 10 meters. If the wagonwheel is unlocked and is now allowed to fall off, will it fall off the loop-the-loop and crash

before reaching the top? A specific value for the radius “r” of the wagonwheel is not needed, nor is the wagonwheel’s mass.

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