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A circular hula hoop rolls upright without slipping on a flat horizontal surface. Which one of the following statements is necessarily true?

a) The hoop's center of mass accelerates.

b) The hoop's kinetic energy decreases.

c) The hoop's angular velocity increases.

d) The hoop's angular momentum is conserved.

User Phoxis
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Final answer:

The necessarily true statement about a circular hula hoop rolling without slipping on a flat surface is that the hoop's angular momentum is conserved, due to the principle of conservation of angular momentum.

Step-by-step explanation:

When a circular hula hoop rolls upright without slipping on a flat horizontal surface, the statement that is necessarily true is: (d) The hoop's angular momentum is conserved. This is due to the principle of conservation of angular momentum, which states that if no external torques act on a system, its angular momentum remains constant.

For the other options: (a) The center of mass may accelerate if there is a net force, but there is not enough information to make this a necessity. (b) The kinetic energy does not necessarily decrease; it would remain constant if rolling at a constant speed. (c) Angular velocity would not necessarily increase unless there was an unbalanced torque applied.

User Jdbs
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