Diagnostic · Motion in 2D
Projectile & Circular Diagnostic
Maps the misconceptions of two-dimensional motion, such as component independence, the centripetal role and the centrifugal ghost, and shows which band your class's answers point to.
IB DP · AP · A-Level · GCSE / IGCSE
1
Forms
30
Questions
32–36
Minutes
11 + lens
Bands
FundaFirst HS diagnostics have run in classrooms at 10 schools · 9 countries · 3 continents
The wrong ideas come from physics education research, which has recorded them since the 1970s: Viennot, Trowbridge & McDermott, Arons, Hestenes, Maloney. The physics comes from Arons, Knight, Moore, and Chabay & Sherwood.
What it maps
Eleven misconception bands across motion in two dimensions, plus one lens.
P1
Component Independence
Horizontal and vertical motion run on their own, and that is two separate claims. The wrong options let the horizontal motion lengthen or shorten the fall.
P2
Projectile Acceleration = g Down
In free flight the acceleration is g, straight down, at every instant, including the top. The turning-point error, the tilted acceleration, and the force of the throw kept alive.
P3
Trajectory and Graph against Path
A height against time graph is not the path through space. Two launch angles that add to 90 degrees give the same range at the same speed.
P4
Mass Independence and Drag
In a vacuum every mass falls with a = g. In air, only drag, which depends on the object, breaks the tie. Reported as provisional only.
C-K1
Circular Acceleration, and Why
At constant speed the velocity still changes direction, so the acceleration is real and points inward. The reason is kinematic: over a short interval the change in velocity points to the centre.
C-K2
Period and Angular to Linear
Rim speed is circumference over period, v = 2πr/T. Angular displacement counts the whole turning history. Reported as provisional only.
C-D0
Curving Needs Inward, Release to Tangent
With no force, motion is straight along the tangent on release. The curved-tube error, where the marble is expected to keep curving after it leaves the tube.
C-D1
Net Inward Force Is a Role
The core band. A real force, or a component of one, supplies the inward net force. Centripetal names the role it plays. It is not an extra force. The fourth arrow, and the belief that only a pull can be centripetal.
C-D2
Vertical Circle & Passive Force
A passive contact force cannot pull. A negative normal force means loss of contact, and at the minimum speed at the top gravity alone supplies the inward force.
C-D3
No Centrifugal Force
Seen from the ground there is no outward force. The passenger carries straight on and the door pushes inward. The third-law partner of the inward pull acts on the string, and not on the object.
C-D4
Banked Curve
Take one axis horizontal, toward the centre, because the net force points that way. Below the design speed, static friction acts up the slope. The banking angle does not depend on mass.
LENS
The Acceleration-Direction Lens
One wrong idea tracked across both families: acceleration points where you are going. Reported only when it shows in both the projectile and the circular questions. When it fires it is treated first, because so much of the topic rests on it.
A question from it
Good marks in two-dimensional motion hide these ideas more often than in any other topic.
The sideways ball stays up longer
Release one ball from rest and launch a second horizontally from the same table height at the same instant. Many students say the launched ball stays up longer, or that a faster launch changes the fall time. They are letting horizontal motion change the vertical fall. It cannot. Gravity alone governs the fall, and the two balls land together.
At the top it stops, so gravity pauses
A stone thrown at an angle reaches the top of its arc. Ask for its acceleration there and many students answer zero, because the stone has stopped rising. Others keep a forward force of the throw alive in flight. Once the stone leaves the hand the only force on it is gravity. The acceleration is g, straight down, the whole time, including the top, where the speed is not zero.
The fourth arrow
Ask the class to draw every force on a puck whirled on a string in a horizontal circle. Three arrows belong, for tension, gravity and the normal force. In many diagrams a fourth appears, an inward arrow labelled centripetal force, beside the tension that already does the job. Centripetal names the role a real force plays, and there is no extra force. This is the core misconception of circular motion.
Something throws me outward
A car takes a sharp left turn and the passenger is pressed against the right-hand door. Ask what pushed them outward and most students name a centrifugal force. Seen from the ground, nothing pushes the passenger outward. The passenger carries straight on, while the car turns left under them. The door comes across and runs into the passenger, pushing them inward.
How it runs
Students use one shared link and need no logins.
30 questions, about 32–36 minutes, no calculator required, single sitting.
The report arrives within 48 hours of your class finishing.
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Arons and Knight document the misconceptions. Moore and Chabay & Sherwood supply the physics treatment.