Final answer:
A hot air balloon moving at 30 degrees east of north with no net force is the only valid inertial frame of reference in the examples provided, because it is moving with constant velocity and not experiencing acceleration, aligning with the definition of an inertial frame where Newton's laws hold true.
Step-by-step explanation:
When considering which is a valid inertial frame of reference, we need to remember that an inertial frame is one where Newton's laws hold true and all forces are real, not fictitious. Examining the options provided, the only scenario that fits this definition is:
- A hot air balloon moving at 30 degrees east of north with no net force is valid because it is moving with a constant velocity, meaning there is no acceleration and hence, no net force acting upon it. This aligns with the definition of an inertial frame of reference where Newton's first law — an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force — applies straightforwardly.
The other scenarios do not align with the definition of an inertial frame:
- A frictionless spinning merry-go-round is not valid because it involves circular motion, requiring a centripetal force, and an observer on the merry-go-round would feel a fictitious centrifugal force, indicating the presence of acceleration hence a non-inertial frame.
- A falling rock is not valid because it is accelerating due to gravity, which makes it a non-inertial frame.
- A space shuttle whose boosters just ignited for takeoff is not valid because it is undergoing acceleration, also indicating a non-inertial frame.
The notion of a valid inertial frame is crucial for making sense of physical phenomena without introducing fictitious forces that would complicate the equations of motion.