An observer in an inertial frame watches a ball roll across a rotating merry-go-round. From the inertial observer's perspective, what does the ball's path look like?
ACurved to the right, because the Coriolis force deflects it
BA straight line, because no real horizontal forces act on the ball
CCurved inward toward the center due to centripetal force
DSpiraling outward due to the centrifugal force
From the inertial frame, Newton's first law applies: the ball moves in a straight line because no real horizontal force acts on it (ignoring friction). The Coriolis and centrifugal forces are pseudo-forces — they exist only in the rotating frame's equations of motion. An observer standing above the merry-go-round would see a straight-line trajectory. An observer *on* the merry-go-round would see a curved path and would need to introduce the Coriolis force to explain it within their (non-inertial) reference frame.
Question 2 Multiple Choice
A stationary object rests on a rotating platform. In the rotating frame, the object appears to experience an outward push. What pseudo-force accounts for this, and why does it appear?
AThe Coriolis force, because the object is moving relative to the inertial frame
BThe centrifugal force, because the rotating frame continuously accelerates the object inward, requiring a compensating outward pseudo-force
CThe centripetal force, which acts outward in rotating frames
DNo pseudo-force is needed; the object is genuinely accelerating outward
In the inertial frame, keeping an object on a circular path requires centripetal force directed inward. In the rotating frame, the object is stationary — so by Newton's second law as applied in that frame, the net force must be zero. The centripetal force still acts inward, so to balance it, we introduce the centrifugal pseudo-force F_cf = mω²r directed outward. The centrifugal force is not real — it appears only because the frame is rotating. The Coriolis force (option A) acts only on objects that are *moving* within the rotating frame; a stationary object experiences no Coriolis force.
Question 3 True / False
The Coriolis force is zero for an object that is stationary within the rotating frame.
TTrue
FFalse
Answer: True
The Coriolis force is F_cor = −2m(ω × v), where v is the velocity of the object as measured in the rotating frame. If the object is stationary in the rotating frame, v = 0, so F_cor = 0. Only objects that are moving within the rotating frame experience a Coriolis deflection. This is why the Coriolis effect is important for large-scale atmospheric motion (where air masses move over great distances) but negligible for everyday objects at rest on Earth's surface.
Question 4 True / False
The centrifugal force felt by a person on a spinning carousel is a real force that acts on them in both the rotating frame and the inertial frame.
TTrue
FFalse
Answer: False
The centrifugal force is a pseudo-force — it exists only in the rotating (non-inertial) frame. In the inertial frame, there is no centrifugal force. What exists in the inertial frame is the centripetal force (e.g., friction or the normal force from the carousel seat) directed inward, which keeps the person on their circular path. In the rotating frame, this same centripetal force points inward and is 'balanced' by the outward centrifugal pseudo-force. The person feels pushed outward because the seat is pushing them inward.
Question 5 Short Answer
Why are pseudo-forces like the centrifugal and Coriolis forces introduced when analyzing motion in a rotating frame? What problem do they solve?
Think about your answer, then reveal below.
Model answer: Newton's second law F = ma holds only in inertial (non-accelerating) frames. In a rotating frame, objects appear to accelerate or curve even when no real force acts on them — because the frame itself is continuously changing direction. If you try to apply F = ma in a rotating frame using only real forces, the equations are wrong: they predict zero acceleration for objects that appear to be moving (from the rotating frame's perspective). Pseudo-forces are mathematical correction terms added to make Newton's second law hold formally in the rotating frame. The centrifugal force corrects for the frame's rotational acceleration on stationary objects; the Coriolis force corrects for the additional deflection experienced by moving objects.
The key insight is that pseudo-forces are bookkeeping devices, not physical forces — they have no source and don't appear in free-body diagrams drawn from inertial frames. Their value is purely computational: they let engineers and scientists use familiar Newtonian analysis in non-inertial frames like Earth's surface without constantly transforming to the inertial frame.