AP Physics 1

What people get wrong

1. Treating speed and velocity as interchangeable. Speed is the magnitude of velocity and is always positive; velocity carries direction and can be negative. Always ask whether the question wants magnitude only or a signed/directional answer.
2. Applying the four kinematic equations when acceleration is not constant (e.g., during a curved velocity-time graph). Instead, use the definitions of average velocity/acceleration or read slopes and areas directly off the graph.
3. Assuming horizontal velocity changes during projectile motion. In the absence of air resistance, a_x = 0, so horizontal velocity is constant throughout the flight — only vertical velocity changes.
4. Forgetting to decompose the initial velocity into components when a projectile is launched at an angle, and mistakenly plugging the full speed into the vertical equations. Always split into v0x and v0y first.

What people get wrong

1. Using $mg$ as the normal force on an incline instead of $mg\cos\theta$. Always find the normal force by balancing forces perpendicular to the incline's surface, not the horizontal.
2. Applying $f_k = \mu_kN$ to an object that is not actually sliding. Check whether the applied force exceeds $\mu_sN$ first; if it doesn't, the object stays at rest and friction equals the applied force, not $\mu_kN$.
3. Pairing the normal force and weight as a Newton's third law pair because they're equal and opposite. They act on the same object and are different types of force, so they cannot be a third-law pair; true pairs act on different objects.
4. Treating 'centripetal force' as an extra force to add to the free-body diagram. It is not a new force — it's the label for the net force (or the net radial component of existing forces) that must point toward the center.

What people get wrong

1. Forgetting the $\cos\theta$ factor when a force isn't parallel to displacement, treating $W=Fd$ even when the force is applied at an angle. Always identify the angle between the force vector and the displacement vector first.
2. Assuming forces like the normal force or the tension in circular motion do work simply because they are large. If a force is perpendicular to the object's displacement at every instant, it does exactly zero work.
3. Using the length traveled along an incline instead of the vertical height change when computing gravitational potential energy. Only $\Delta h$ (vertical) matters for $\Delta PE_{grav}$, not the path length.
4. Applying $KE_i+PE_i=KE_f+PE_f$ when friction or another non-conservative force is present. Check the force list first; if friction acts, add a $W_{nc}$ term or the answer will overestimate final speed or height.

What people get wrong

1. Treating momentum as a scalar and dropping signs. Fix: pick one positive direction before writing any equation, and give every velocity (including 'at rest' as zero) a signed value consistent with that choice.
2. Assuming kinetic energy is conserved in every collision. Fix: only assume KE conservation if the problem explicitly states 'elastic' or you have verified it by calculation; otherwise treat KE as unknown and solve using momentum alone.
3. Applying conservation of momentum to a system that isn't isolated, such as ignoring friction, an incline, or an external push during the interaction. Fix: check that the net external force is zero (or that the interaction time is short enough that external impulses are negligible) before conserving momentum.
4. Confusing impulse with force. Fix: remember impulse is $F\Delta t$, a quantity that depends on both the force and how long it acts; a small force over a long time can deliver the same impulse as a large force over a short time.

What people get wrong

1. Using the full distance r in torque instead of the lever arm — a force applied at an angle to the object contributes only its perpendicular component. Always multiply by $\sin\theta$, or find the true perpendicular distance from the axis to the force's line of action.
2. Assuming equilibrium is satisfied once $\sum F=0$ is checked. Rotational equilibrium requires $\sum \tau=0$ as a separate, independent condition — a pair of equal and opposite forces on opposite ends of an object can satisfy $\sum F=0$ while still spinning the object up.
3. Treating rotational inertia as if it only depended on total mass. Two objects with identical mass and radius (a disk and a hoop) have very different I because the hoop's mass sits farther from the axis on average — always check how mass is distributed, not just how much there is.
4. Losing track of sign convention when several torques act. Pick counterclockwise (or clockwise) as positive once, and apply it consistently to every torque in the equation, including ones that seem 'obviously' negative.

What people get wrong

1. Computing only $\frac12mv^2$ for a rolling object's kinetic energy. Instead, always add the rotational term $\frac12I\omega^2$ using the rolling constraint $\omega=v/r$.
2. Assuming angular speed stays constant when moment of inertia changes (e.g., a skater pulling in arms). Instead, recognize that angular momentum $L=I\omega$ is what's conserved, so $\omega$ must increase as $I$ decreases.
3. Using $L=mvr$ even when the velocity isn't perpendicular to the position vector. Instead, use $L=mvr\sin\theta$, or identify the perpendicular distance (lever arm) directly.
4. Treating the static friction force in rolling-without-slipping problems as if it dissipates energy. Instead, remember static friction does zero work (the contact point has zero velocity), so mechanical energy is still conserved.

What people get wrong

1. Assuming a larger amplitude makes the period longer or shorter. For ideal SHM (spring or small-angle pendulum), period depends only on m,k or L,g — never on amplitude. Check the formula, not intuition, before answering period questions.
2. Thinking speed is maximum at the turning points (x = ±A). Speed is actually zero there and maximum at equilibrium (x = 0); acceleration is the one that's maximum at the extremes. Sketch the motion before assigning max/min values.
3. Mixing up which variables affect which period. Mass matters for a spring's period but not for a pendulum's; length matters for a pendulum but has no meaning for a spring. Always match the formula to the physical system.
4. Applying the small-angle pendulum formula T = 2π√(L/g) to large swing angles. The formula breaks down above roughly 15°, and the real period becomes amplitude-dependent — don't assume the simple formula always holds.

What people get wrong

1. Forgetting the atmospheric pressure term when a problem asks for absolute pressure at a depth. Instead, always check whether the question wants gauge pressure (just $\rho g h$) or absolute pressure (must add $P_0$).
2. Using mass instead of weight in buoyancy problems, e.g. computing $F_b=\rho V$ and forgetting the factor of $g$. Instead, always write $F_b=\rho_{fluid}V_{displaced}g$ and check units come out in newtons.
3. Assuming buoyant force depends on the object's own density or weight. Instead, remember buoyant force depends only on the fluid's density and the volume displaced — the object's density only determines whether it floats or sinks.
4. Mixing up which area is A1 and which is v1 in the continuity equation, leading to an inverted answer (getting a slower speed in the narrower section). Instead, remember flow speeds up where the pipe narrows: smaller area always pairs with larger speed.