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AP Physics C: Mechanics multiple-choice practice 22 questions with answers

Written by STEM-Tutor's tutors · Updated October 2026 · 22 questions

Free AP Physics C: Mechanics multiple-choice questions in the style of the real exam. Click an answer and it is marked straight away; then open the hint or the worked solution, one step at a time.

On this page
  1. How the section works
  2. 22 multiple-choice questions
  3. Tips
  4. After the questions
  5. FAQ

How the AP Physics C: Mechanics multiple-choice section works

From May 2027 the multiple-choice section has 42 questions: 42 questions in 85 minutes. It is worth 50% of your AP score, there is no penalty for a wrong answer, and each question has four options.

The questions below cover every unit. Give yourself about two minutes a question.

22 multiple-choice questions

Q1Warm-up
At the highest point of a projectile's path, with no air resistance:

Hint

Which component of velocity changes, and which does not?

Worked solution
  1. The vertical velocity is zero at the top, but the horizontal velocity is unchanged.
  2. So the velocity is horizontal, while the acceleration is still g downwards: C.
Q2Exam-style
A particle moves with x(t) = t3 − 6t2 + 9t. At what times is it momentarily at rest?

Hint

At rest means v = 0.

Worked solution
  1. v = 3t2 − 12t + 9 = 3(t − 1)(t − 3).
  2. v = 0 at t = 1 s and t = 3 s: B.
Q3Warm-up
The Earth pulls down on a book with its weight. What is the Newton's third law partner of this force?

Hint

Third-law pairs act on two different objects and are the same type of force.

Worked solution
  1. The pair of “Earth pulls book (gravity)” is “book pulls Earth (gravity)”.
  2. The answer is B. The table's push is a different force on the same object.
Q4Warm-up
A block slides along a horizontal floor. How much work does the normal force do on it?

Hint

Work depends on the angle between force and displacement.

Worked solution
  1. The normal force is perpendicular to the displacement, so cos 90° = 0.
  2. It does zero work: C.
Q5Exam-style
On a graph of potential energy U against position x, a particle is in stable equilibrium where:

Hint

F = −dU/dx. What does the force do if the particle moves slightly away?

Worked solution
  1. At a minimum, dU/dx = 0, so F = 0.
  2. Moving either way makes F point back towards the minimum, so the equilibrium is stable: B.
Q6Warm-up
In a perfectly elastic collision between two objects:

Hint

Momentum is conserved in every collision with no external impulse.

Worked solution
  1. Momentum is always conserved here; elastic means kinetic energy is conserved too.
  2. The answer is C.
Q7Warm-up
A system has no net external force on it. Its centre of mass:

Hint

ΣFext = Macm.

Worked solution
  1. With no external force, acm = 0.
  2. So the centre of mass moves with constant velocity (which may be zero): B.
Q8Warm-up
A hoop and a solid disk have the same mass and radius. Which has the greater rotational inertia about its central axis?

Hint

Rotational inertia grows with mass placed far from the axis.

Worked solution
  1. All of the hoop's mass is at radius R; much of the disk's is closer in.
  2. Ihoop = MR2 > Idisk = ½MR2: A.
Q9Exam-style
A solid sphere and a hoop are released from rest at the top of the same incline and roll without slipping. Which reaches the bottom first?

Hint

The one with less of its energy going into rotation moves faster.

Worked solution
  1. The sphere has I = (2/5)MR2, the hoop MR2.
  2. The sphere puts a smaller share of its energy into rotation, so it moves faster and arrives first: A.
Q10Warm-up
A spinning ice skater pulls her arms in. What happens?

Hint

There is no external torque about her axis.

Worked solution
  1. L = Iω is conserved, and I decreases, so ω increases.
  2. The answer is B. Her kinetic energy increases, from the work her arms do.
Q11Exam-style
A particle moves in a straight line at constant velocity, not through point P. Its angular momentum about P:

Hint

τ = dL/dt. Is there a torque about P?

Worked solution
  1. No net force acts, so there is no torque about P.
  2. So L = mvr⊥ is constant, with r⊥ the fixed perpendicular distance from P to the line: C.
Q12Warm-up
In simple harmonic motion, the magnitude of the acceleration is greatest:

Hint

a = −ω2x.

Worked solution
  1. The acceleration is proportional to the displacement.
  2. So it is greatest at maximum displacement: B.
Q13Exam-style
The amplitude of a mass-spring oscillator is doubled. What happens to its period?

Hint

Look at T = 2π√(m/k). Does A appear?

Worked solution
  1. The period depends only on m and k.
  2. So it stays the same: C. The maximum speed doubles instead.
Q14Warm-up
A particle moves with v(t) = 3t2 − 2t m/s and x(0) = 0. Where is it at t = 2 s?

Hint

Integrate v(t) to get x(t).

Worked solution
  1. x(t) = t3 − t2 + C, and x(0) = 0 gives C = 0.
  2. x(2) = 8 − 4.
  3. x = 4 m. The answer is A.
Q15Warm-up
A force F(x) = 6x N acts on an object as it moves from x = 0 to x = 2 m. How much work does the force do?

Hint

W = ∫ F dx.

Worked solution
  1. W = ∫02 6x dx = [3x2]02.
  2. = 3(4) = 12 J.
  3. The answer is B.
Q16Exam-style
What is the rotational inertia of a uniform rod of mass 3 kg and length 2 m about an axis through one end, perpendicular to the rod?

Hint

For a rod about one end, I = (1/3)ML2, which you can derive from ∫ r2 dm.

Worked solution
  1. I = ∫0L r2 (M/L) dr = (1/3)ML2.
  2. I = (1/3)(3)(22) = 4 kg·m2.
  3. The answer is B. (1 kg·m2 is the value about the centre.)
Q17Exam-style
A solid cylinder rolls without slipping from rest down a ramp, dropping 0.9 m in height. Using g = 9.8 m/s2, how fast is it moving at the bottom?

Hint

Energy is shared between translation and rotation. For a solid cylinder, I = (1/2)MR2.

Worked solution
  1. Mgh = (1/2)Mv2 + (1/2)(1/2 MR2)(v/R)2 = (3/4)Mv2.
  2. v = √(4gh/3) = √(4 × 9.8 × 0.9/3) = √11.76.
  3. v ≈ 3.43 m/s. (4.20 m/s would be sliding with no rotation.) The answer is A.
Q18Exam-style
A 0.2 kg object falls through a fluid with a drag force F = −bv, where b = 0.5 kg/s. Using g = 9.8 m/s2, what is its terminal speed?

Hint

At terminal speed the net force is zero.

Worked solution
  1. At terminal speed, bv = mg.
  2. v = mg/b = (0.2)(9.8)/0.5.
  3. v = 3.92 m/s. The answer is A.
Q19Warm-up
A force F(t) = 4t N acts on an object from t = 0 to t = 3 s. What impulse does it deliver?

Hint

Impulse J = ∫ F dt.

Worked solution
  1. J = ∫03 4t dt = [2t2]03.
  2. = 2(9) = 18 N·s.
  3. The answer is B.
Q20Warm-up
A skater spins at 3 rad/s with rotational inertia 4 kg·m2, then pulls in their arms so the rotational inertia drops to 2 kg·m2. What is the new angular speed?

Hint

With no external torque, angular momentum is conserved.

Worked solution
  1. I1ω1 = I2ω2.
  2. (4)(3) = (2)ω2.
  3. ω2 = 6 rad/s. The answer is C.
Q21Challenge
A uniform rod 1.5 m long swings with small oscillations about a pivot at one end. Using g = 9.8 m/s2, what is its period?

Hint

A physical pendulum has T = 2π√(I/(mgd)), where d is the distance from the pivot to the centre of mass.

Worked solution
  1. I = (1/3)mL2 and d = L/2, so I/(mgd) = 2L/(3g).
  2. T = 2π√(2 × 1.5/(3 × 9.8)) = 2π√0.102.
  3. T ≈ 2.01 s. (2.46 s is a simple pendulum of the same length.) The answer is A.
Q22Warm-up
A constant 50 N force pushes a box at a steady 4 m/s in the direction of the force. What power does the force deliver?

Hint

P = Fv when the force is along the velocity.

Worked solution
  1. P = Fv.
  2. P = (50)(4) = 200 W.
  3. The answer is B.

Tips for the AP Physics C: Mechanics multiple-choice section

After the questions

Note every question you missed and its topic, then practise that unit: AP Physics C: Mechanics practice by unit. For a full timed test, take the practice exam, then put your score into our AP Physics C: Mechanics score calculator. For the free-response section, use the official AP Physics C: Mechanics past papers.

Frequently asked questions

Are these real AP Physics C: Mechanics exam questions?

No. They are original questions written by our tutors in the style of the exam, so each one can have a full worked solution. For real exam questions, use the official AP Physics C: Mechanics past papers.

How many multiple-choice questions are on the AP Physics C: Mechanics exam?

From May 2027, 42: 42 questions in 85 minutes. The multiple-choice section is 50% of your score.

Is there a penalty for wrong answers?

No. Only correct answers count, so answer every question, even if you have to guess.