Past free-response questions

2026

• Question 1 · Mathematical Routines · 10 points Water droplets from a fountain nozzle Sketch the velocity components of a droplet in flight, derive the launch speed from the peak height, derive the flow rate, and decide how the peak height changes with a narrower nozzle at the same flow rate. Unit 1, Unit 8
• Question 2 · Translation Between Representations · 12 points Two disks colliding on a track Draw momentum vectors after a collision, derive the struck disk's kinetic energy, extend position graphs for both disks and the center of mass, and compare their momentum changes. Unit 4, Unit 2
• Question 3 · Experimental Design and Analysis · 10 points Measuring friction with a sliding block Plan meterstick measurements and a linear graph to find a friction coefficient, then linearize ramp distance and speed data, plot it with a best fit line, and calculate the coefficient. Unit 2, Unit 3, Unit 1
• Question 4 · Qualitative Quantitative Translation · 8 points Two spinning toys pulled by strings Compare the final angular speeds of two toys with different rotational inertia spun by the same string pull, derive one toy's angular speed, and check the derivation against the comparison. Unit 6, Unit 5

2025

• Question 1 · Mathematical Routines · 10 points Block dropped onto a moving cart Sketch the system's momentum over time, derive the final speed and the kinetic energy lost when a block lands and sticks on a cart, and decide whether momentum changes when a block slides before moving with the cart. Unit 4
• Question 2 · Translation Between Representations · 12 points Block sliding down a ramp into a spring Fill in energy bar charts at two positions, derive the spring constant from energy conservation, sketch total and gravitational energy against position, and compare speeds at two points using those sketches. Unit 3
• Question 3 · Experimental Design and Analysis · 10 points Balancing a meterstick to find masses Design a balancing procedure to find a block's mass with a linear graph, then linearize tension and angle data for a horizontal meterstick, plot it, draw a best fit line, and find the meterstick's mass. Unit 5
• Question 4 · Qualitative Quantitative Translation · 8 points Block rising in fresh and salt water Compare the upward acceleration of a released block in fresh water and salt water using the forces on it, derive the acceleration from Newton's second law, and check the result against the comparison. Unit 8, Unit 2

2024

This exam had five free-response questions in 90 minutes, worth 7 or 12 points each. The current exam has 4 free-response questions in 95 minutes. The skills these questions practice still count.

• Question 1 · Short Answer · 7 points Block sliding through loops on a track Complete an energy bar chart at the top of a loop, derive the block's speed there from energy conservation, draw the forces at the top of a second loop, and explain why a claimed minimum release height is wrong. Unit 3, Unit 2
• Question 2 · Experimental Design · 12 points Finding a spring constant by oscillation Plan an experiment with hanging masses, a stopwatch and a scale to find a spring constant, choose axes for a linear graph, then use velocity and force graphs of an oscillating cart to find kinetic energy and momentum changes. Unit 7, Unit 3, Unit 4
• Question 3 · Qualitative/Quantitative Translation · 12 points Hinged beam held up by a string Draw the forces on a horizontal beam, compare the string tension for two attachment points, derive the tension from torques, check consistency, and sketch angular speed after the string is cut. Unit 5
• Question 4 · Paragraph · 7 points Pendulum taken to other planets Explain why gravity does less work on a pendulum on a larger planet, then write a paragraph on how a slightly stretchy pendulum's period could go either up or down on a heavier planet. Unit 7, Unit 2, Unit 3
• Question 5 · Short Answer · 7 points Two blocks in an elastic collision Find a block's speed after an elastic collision from its kinetic energy change, extend position graphs for both blocks and the center of mass, and explain how the center of mass line changes if the blocks stick. Unit 4, Unit 2

2023

This exam had five free-response questions in 90 minutes, worth 7 or 12 points each. The current exam has 4 free-response questions in 95 minutes. The skills these questions practice still count.

• Question 1 · Short Answer · 7 points Cart on a spring with a dropped block Explain an energy graph for an oscillating cart and spring, find how the frequency changes after a block lands and sticks on the cart, and sketch the kinetic energy of a smaller system. Unit 7, Unit 3, Unit 2
• Question 2 · Experimental Design · 12 points Cart rolling down a ramp experiment Linearize position and time data to get the cart's acceleration, work out g from it, explain why the measured g comes out low, and sketch position and velocity graphs for a cart pushed up the ramp. Unit 1, Unit 2
• Question 3 · Quantitative/Qualitative Translation · 12 points Block on a spring whirled in a circle Compare the spring force at two stretches, decide which speed is larger, derive the block's speed from the spring force acting as the centripetal force, and check the equation against the earlier reasoning. Unit 2
• Question 4 · Short Answer Paragraph Argument · 7 points Disk and hoop pulleys pulled by strings Find the angular acceleration of a disk pulley from the string tension, then write a paragraph explaining why a disk and a hoop gain equal angular momentum but unequal rotational kinetic energy. Unit 5, Unit 6
• Question 5 · Short Answer · 7 points Rod and sphere falling over on an axle Use video frames to pick where angular acceleration and rotational kinetic energy are largest, derive the kinetic energy gained as the rod swings down, and explain the gain without Earth in the system. Unit 5, Unit 6, Unit 3

2022

This exam had five free-response questions in 1 hour and 30 minutes: Questions 1, 4 and 5 were short questions worth 7 points each with about 13 minutes suggested, and Questions 2 and 3 were long questions worth 12 points each with about 25 minutes suggested. The current exam has 4 free-response questions in 95 minutes. The skills these questions practice still count.

• Question 1 · Short Answer · 7 points Spring and hanging block energy bar charts Explain in terms of forces why a hanging block first speeds up and then stops, derive how far it falls before stopping, and fill in an energy bar chart for the case with friction. Unit 3, Unit 2
• Question 2 · Qualitative/Quantitative Translation · 12 points Net gravitational force on two moons Draw the forces on two aligned moons, argue both ways about which feels the larger net force, then write expressions for each net force and check them against the arguments. Unit 2
• Question 3 · Experimental Design · 12 points Falling block spinning a wheel, energy experiment Plan a measurement comparing a falling block's kinetic energy gain with the drop in gravitational energy, sketch the wheel's rotational energy, and find the wheel's rotational inertia from a best fit line. Unit 6, Unit 3, Unit 5
• Question 4 · Short Answer Paragraph Argument · 7 points Sticking clay versus bouncing ball collisions Draw the momentum of a ball and block system after a bouncing collision compared with a sticking one, then argue in a paragraph which struck block lands farther from the table. Unit 4, Unit 1
• Question 5 · Short Answer · 7 points Oscillating spring read by motion detector Use a position graph from a motion detector to find a spring constant, explain why energies match at two times, and predict and graph the motion with a stiffer spring. Unit 7, Unit 2

2021

This exam had five free-response questions in 1 hour and 30 minutes: Questions 1, 4 and 5 were short questions worth 7 points each with about 13 minutes suggested, and Questions 2 and 3 were long questions worth 12 points each with about 25 minutes suggested. The current exam has 4 free-response questions in 95 minutes. The skills these questions practice still count.

• Question 1 · Short Answer · 7 points Stunt cyclist ramp jump over cars Derive how far a cyclist travels through the air after coasting down a ramp, use it to predict the effect of a taller ramp, and sketch vertical velocity against time during the jump. Unit 3, Unit 1
• Question 2 · Experimental Design · 12 points Rod thickness and breaking force models Plan an experiment to decide whether the force that breaks a plastic rod depends on its radius or its cross sectional area, sketch both models, then graph given data and pick the better model. Unit 2
• Question 3 · Qualitative/Quantitative Translation · 12 points Student pushing disk, then disk collision Find the speeds of a student and a disk after a push using impulse and momentum, sketch both speeds against time, then reason about and derive the center of mass speed after a sticking collision. Unit 4, Unit 2
• Question 4 · Paragraph-Length Response · 7 points Rolling cylinder and sliding block on inclines Sketch a rolling cylinder's total kinetic energy against distance traveled, then explain with energy why it and a block on a rough incline reach the bottom at the same speed. Unit 6, Unit 3
• Question 5 · Short Answer · 7 points Two joined pulleys with hanging objects Find the net torque on a two pulley system with hanging masses, explain the motion, compare angular velocity and acceleration after one string is cut, and graph angular velocity over time. Unit 5

2019

This exam had five free-response questions in 90 minutes: Questions 1, 4 and 5 were short questions worth 7 points each with about 13 minutes suggested, and Questions 2 and 3 were long questions worth 12 points each with about 25 minutes suggested. The current exam has 4 free-response questions in 95 minutes. The skills these questions practice still count.

• Question 1 · Short free-response · 7 points Blocks colliding across a rough patch Sketch the speed of a two block system's center of mass through a push, a rough region and a sticking collision, then decide where a pushed sphere's angular momentum changes. Unit 4, Unit 2, Unit 1, Unit 6
• Question 2 · Long free-response · 12 points Table block pulled by hanging block Estimate the acceleration of a table block and a hanging block in extreme mass cases, draw free body diagrams, derive the acceleration, check it against the estimates, and compare tensions with a massive pulley. Unit 2, Unit 5
• Question 3 · Long free-response · 12 points Testing a spring launcher's spring constant Choose a principle and plan an experiment with a spring launcher to test whether its spring constant stays the same for different compressions, then sketch launch speed against sphere mass. Unit 3, Unit 2
• Question 4 · Short free-response · 7 points Motor lifting a block, circuit choice Write the mechanical power a motor delivers lifting a block, then argue in a paragraph where to add a resistor so the lift takes less time. Unit 3
• Question 5 · Short free-response · 7 points Resonating air in an open tube Find the length of an open tube that resonates with a tuning fork, sketch how the air's maximum speed varies along the tube, and find the new frequency when one end is closed in another gas.

2018

This exam had five free-response questions in 90 minutes: Questions 1, 4 and 5 were short questions worth 7 points each with about 13 minutes suggested, and Questions 2 and 3 were long questions worth 12 points each with about 25 minutes suggested. The current exam has 4 free-response questions in 95 minutes. The skills these questions practice still count.

• Question 1 · Short free-response · 7 points Spacecraft in a circular orbit Draw the forces on an orbiting spacecraft, derive its orbital period, and decide how the period and speed change with a heavier craft or a larger orbit. Unit 6, Unit 2
• Question 2 · Long free-response · 12 points Resistivity of conductive dough cylinders Choose what to graph to find the resistivity of dough cylinders, plot and use the data, decide whether shape matters, and plan a test of whether resistivity depends on temperature.
• Question 3 · Long free-response · 12 points Spinning disk slowed by axle friction Sketch angular velocity and angular acceleration for a disk slowed by constant friction, derive its rotational inertia, redo the sketches when oil reduces the friction, and pick a plausible torque model. Unit 5
• Question 4 · Short free-response · 7 points Dots on a transverse wave Show the velocity and acceleration of two points on a traveling wave, draw the string a quarter period later, and find how far one point travels in a full period.
• Question 5 · Short free-response · 7 points Block dropped onto an oscillating block Find how the period of a spring and block oscillator changes when a second block lands and sticks, then argue in a paragraph how the amplitude changes. Unit 7, Unit 4

2017

This exam had five free-response questions in 90 minutes: Questions 1, 4 and 5 were short questions worth 7 points each with about 13 minutes suggested, and Questions 2 and 3 were long questions worth 12 points each with about 25 minutes suggested. The current exam has 4 free-response questions in 95 minutes. The skills these questions practice still count.

• Question 1 · Short free-response · 7 points Identical bulbs in three circuits Rank the voltages across bulbs in series and parallel circuits, then argue in a paragraph which battery runs out of energy first and which lasts longest.
• Question 2 · Long free-response · 12 points Measuring static friction, block on board Design and diagram an experiment to find the coefficient of static friction, derive it from the measurements, judge class data comparing static and kinetic friction, and predict the effect of extra mass. Unit 2
• Question 3 · Long free-response · 12 points Disk sticking to a pivoted rod Reason about where a sliding disk should hit a pivoted rod to spin it fastest, test two proposed equations for plausibility, derive the angular speed, and compare a bounce with a stick. Unit 6, Unit 5
• Question 4 · Short free-response · 7 points Blocks launched off slides from tables Decide whether blocks leaving differently built slides hit the floor equally far from their tables, then compare landing distance and landing time for two slide shapes. Unit 3, Unit 1
• Question 5 · Short free-response · 7 points Two wave pulses passing on a string Plot the velocity of one point on a string as a pulse passes it, then sketch the string when two opposite pulses fully overlap.

2016

This exam had five free-response questions in 90 minutes: Questions 1, 4 and 5 were short questions worth 7 points each with about 13 minutes suggested, and Questions 2 and 3 were long questions worth 12 points each with about 25 minutes suggested. The current exam has 4 free-response questions in 95 minutes. The skills these questions practice still count.

• Question 1 · Short free-response · 7 points Wheel rolling down a ramp Draw the forces on a rolling wheel and pick the one that changes its spin, derive its acceleration, and compare its speed at the bottom with a sliding block using forces and then energy. Unit 6, Unit 5, Unit 2, Unit 3
• Question 2 · Long free-response · 12 points Testing whether a toy ball bounces elastically Plan an experiment testing whether a ball's bounces become less elastic at higher speeds, describe how to present and judge the data, and give an example result that seems to break a physics principle. Unit 4, Unit 3
• Question 3 · Long free-response · 12 points Cart on a ramp with speed bumps Sketch the velocity of a cart bumping down a long ramp, predict how bump spacing and ramp angle change its top average speed, and test a proposed equation against data and physical sense. Unit 3, Unit 1
• Question 4 · Short free-response · 7 points Four resistors with one removed Rank the voltages across four resistors, then decide how removing one resistor changes the current through two of the others.
• Question 5 · Short free-response · 7 points Standing wave on a hanging rope Explain why the tension is larger higher up a hanging rope, then argue in a paragraph how the standing wave pattern shows that more tension means faster waves. Unit 2

2015

This exam had five free-response questions in 90 minutes: Questions 1, 4 and 5 were short questions worth 7 points each with about 13 minutes suggested, and Questions 2 and 3 were long questions worth 12 points each with about 25 minutes suggested. The current exam has 4 free-response questions in 95 minutes. The skills these questions practice still count.

• Question 1 · Short free-response · 7 points Two blocks over pulleys, adding a third Draw scaled free body diagrams for two blocks hanging over pulleys, derive the acceleration, and decide how adding a third block on the table changes it. Unit 2
• Question 2 · Long free-response · 12 points Lightbulb and resistor circuit experiment Plan and diagram a circuit experiment showing whether current or energy is used up in a bulb, then extend it to test whether the bulb is nonohmic, considering meter uncertainty.
• Question 3 · Long free-response · 12 points Spring launched block on a rough track Sketch kinetic and spring energy against position for a block launched onto a rough track, judge a student's prediction for doubled compression, and derive the actual stopping point. Unit 3, Unit 2
• Question 4 · Short free-response · 7 points Dropped and launched spheres landing together Draw the forces on a dropped sphere and a horizontally launched sphere, sketch their horizontal velocities, and explain in a paragraph why they land at the same time. Unit 1, Unit 2
• Question 5 · Short free-response · 7 points Strings on oscillators with hanging blocks Explain what makes four similar strings have different fundamental frequencies, decide whether a frequency graph would be linear, and mark the fastest moving points in a second harmonic.