An Inspiring Journey of a Circular Hula Hoop

What makes the circular hula hoop roll upright without slipping on a flat horizontal surface?

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.

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.

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.