Ap Physics C Mechanics Practice Exam 2025

Let's conquer the AP Physics C: Mechanics exam! Mastering this subject requires not just theoretical knowledge but also consistent practice. This comprehensive guide provides a practice exam designed to mirror the format and content of the 2025 AP Physics C: Mechanics exam, equipping you with the tools and confidence to excel.

AP Physics C: Mechanics Practice Exam 2025

This practice exam consists of two sections: Multiple Choice and Free Response. Simulate exam conditions by setting a timer and minimizing distractions. Good luck!

Section I: Multiple Choice (35 Questions, 45 Minutes)

Instructions: The following are single-selection multiple-choice questions. Select the best answer for each question.

A particle moves along the x-axis with a velocity given by v(t) = 3t² - 6t, where t is in seconds and v is in meters per second. What is the acceleration of the particle at t = 2 seconds?

(A) 0 m/s² (B) 6 m/s² (C) 12 m/s² (D) 18 m/s² (E) 24 m/s²
A block of mass m slides down a frictionless inclined plane of angle θ. What is the magnitude of the block's acceleration?

(A) g (B) g sin θ (C) g cos θ (D) g tan θ (E) g cot θ
A projectile is launched with an initial velocity v₀ at an angle θ above the horizontal. Assuming air resistance is negligible, what is the maximum height reached by the projectile?

(A) (v₀² sin θ) / (2g) (B) (v₀² sin² θ) / (2g) (C) (v₀² cos θ) / (2g) (D) (v₀² cos² θ) / (2g) (E) (v₀² tan θ) / (2g)
A force F is applied to a block of mass m on a horizontal surface. The coefficient of kinetic friction between the block and the surface is μk. What is the magnitude of the frictional force acting on the block?

(A) μk * m * g (B) μk * F (C) μk * (F - m * g) (D) μk * (F + m * g) (E) μk * F * g
A wheel of radius R rolls without slipping along a horizontal surface with a constant angular velocity ω. What is the linear speed of a point on the rim of the wheel?

(A) ω (B) Rω (C) ω / R (D) R / ω (E) R²ω
Two objects of masses m₁ and m₂ collide elastically in one dimension. If the initial velocities of the objects are v₁i and v₂i, respectively, what is the final velocity of the first object, v₁f?

(A) (m₁ - m₂) / (m₁ + m₂) * v₁i + (2m₂) / (m₁ + m₂) * v₂i (B) (m₁ + m₂) / (m₁ - m₂) * v₁i + (2m₂) / (m₁ + m₂) * v₂i (C) (2m₁) / (m₁ + m₂) * v₁i + (m₁ - m₂) / (m₁ + m₂) * v₂i (D) (2m₁) / (m₁ + m₂) * v₁i + (m₁ + m₂) / (m₁ - m₂) * v₂i (E) v₁i - v₂i
A simple pendulum of length L oscillates with a small amplitude. What is the period of oscillation?

(A) 2π√(L/g) (B) 2π√(g/L) (C) 2πL/g (D) 2πg/L (E) √(L/g)
A spring with spring constant k is stretched a distance x from its equilibrium position. What is the potential energy stored in the spring?

(A) kx (B) (1/2)kx (C) kx² (D) (1/2)kx² (E) k²x
A solid sphere of mass M and radius R is rotating about an axis through its center with an angular velocity ω. What is the rotational kinetic energy of the sphere? (I = (2/5)MR²)

(A) (1/2)Mω² (B) (1/2)Rω² (C) (1/5)MR²ω² (D) (1/5)Mω² (E) (1/5)MRω
A satellite is in a circular orbit around Earth. If the radius of the orbit is doubled, what happens to the satellite's speed?

(A) It doubles. (B) It is halved. (C) It increases by a factor of √2. (D) It decreases by a factor of √2. (E) It remains the same.
A uniform rod of length L and mass M is pivoted at one end. What is the moment of inertia of the rod about the pivot point? (I_center = (1/12)ML²)

(A) (1/12)ML² (B) (1/6)ML² (C) (1/4)ML² (D) (1/3)ML² (E) (1/2)ML²
A ball of mass m is thrown horizontally with a velocity v and strikes a stationary block of mass M resting on a frictionless surface. The ball rebounds with a velocity -v/2. What is the velocity of the block after the collision?

(A) v (B) (m/M)v (C) (3m/2M)v (D) (2m/3M)v (E) (m/2M)v
A disk rotates with constant angular acceleration. The angular displacement is given by θ = αt² + βt, where α and β are constants. What is the angular velocity at time t?

(A) αt + β (B) 2αt + β (C) αt² + βt (D) α + β (E) 2α + βt
A car travels around a circular track of radius R with a constant speed v. What is the centripetal acceleration of the car?

(A) v²/R (B) vR (C) v/R (D) R/v² (E) v²/R²
A force F = (2i - 3j) N acts on a particle that undergoes a displacement Δr = (5i + j) m. What is the work done by the force?

(A) 7 J (B) 10 J (C) 13 J (D) 17 J (E) 20 J
Which of the following is NOT a conservative force?

(A) Gravitational force (B) Spring force (C) Electrostatic force (D) Frictional force (E) All of the above are conservative forces.
A ladder leans against a smooth wall. The floor is also smooth. What is true about the forces acting on the ladder?

(A) There is a frictional force at both the wall and the floor. (B) There is no frictional force at either the wall or the floor. (C) There is a frictional force only at the wall. (D) There is a frictional force only at the floor. (E) The normal forces at the wall and floor must be equal.
A particle is subject to a force F(x) = -kx³, where k is a positive constant. What is the potential energy function U(x) associated with this force?

(A) (1/2)kx⁴ (B) (1/3)kx⁴ (C) (1/4)kx⁴ (D) -(1/3)kx⁴ (E) -(1/4)kx⁴

A uniform cable of weight W is suspended vertically from one end. What is the tension in the cable at the midpoint?

(A) 0 (B) W/4 (C) W/2 (D) W (E) 2W
A yo-yo is released from rest and allowed to unwind. As it falls, what happens to its translational and rotational kinetic energies?

(A) Translational kinetic energy increases, rotational kinetic energy decreases. (B) Translational kinetic energy decreases, rotational kinetic energy increases. (C) Both translational and rotational kinetic energies increase. (D) Both translational and rotational kinetic energies decrease. (E) Translational kinetic energy remains constant, rotational kinetic energy increases.
A small block is placed on a rotating turntable at a distance r from the center. The coefficient of static friction between the block and the turntable is μs. What is the maximum speed the block can have before it starts to slip?

(A) √(μs * g * r) (B) μs * g * r (C) √(μs * g / r) (D) μs * g / r (E) √(g * r / μs)
A mass is attached to a spring and undergoes simple harmonic motion. If the amplitude of the motion is doubled, what happens to the total energy of the system?

(A) It doubles. (B) It is halved. (C) It quadruples. (D) It remains the same. (E) It increases by a factor of √2.
What is the physical quantity that represents the rotational analog of mass?

(A) Torque (B) Angular velocity (C) Angular acceleration (D) Moment of inertia (E) Angular momentum

A car accelerates uniformly from rest to a speed of 20 m/s in 5 seconds. What is the distance traveled by the car during this time?

(A) 20 m (B) 40 m (C) 50 m (D) 100 m (E) 200 m
A system consists of two particles with masses m and 2m. The position vectors of the particles are r₁ = (i + j) and r₂ = (2i - j), respectively. What is the position vector of the center of mass of the system?

(A) (i - j) (B) (5i - j) (C) (i - 5j) (D) (5/3 i - 1/3 j) (E) (3/5 i - 1/5 j)
A bowling ball collides head-on with a stationary pin. Which of the following quantities is always conserved in this collision?

(A) Kinetic energy (B) Potential energy (C) Momentum (D) Velocity (E) Acceleration

A person stands on a rotating platform. When the person moves towards the center of the platform, what happens to the angular speed of the platform?

(A) It increases. (B) It decreases. (C) It remains the same. (D) It becomes zero. (E) It oscillates.
A rocket is propelled forward by the ejection of exhaust gases. What is the primary principle behind the rocket's propulsion?

(A) Conservation of energy (B) Conservation of momentum (C) Conservation of angular momentum (D) Newton's first law (E) Newton's law of gravitation

A block is pulled along a rough horizontal surface at a constant speed by a force F. The work done by the force F is equal to:

(A) The change in kinetic energy of the block. (B) The change in potential energy of the block. (C) The work done by friction. (D) The negative of the work done by friction. (E) Zero.

A simple harmonic oscillator has a period T. If the mass is doubled, what is the new period?

(A) T/2 (B) T/√2 (C) T (D) T√2 (E) 2T

What is the area under a force versus time graph represent?

(A) Work (B) Power (C) Impulse (D) Energy (E) Momentum

Which of the following statements is true about the gravitational force between two objects?

(A) It is always attractive. (B) It is always repulsive. (C) It can be either attractive or repulsive. (D) It depends on the medium between the objects. (E) It is independent of the masses of the objects.

A string is wrapped around a solid cylinder of mass M and radius R. The cylinder is released from rest. What is the acceleration of the center of mass of the cylinder as it falls?

(A) g (B) (1/2)g (C) (2/3)g (D) (3/4)g (E) (1/3)g
A satellite is in an elliptical orbit around a planet. At which point in the orbit is the satellite's speed the greatest?

(A) At the point farthest from the planet (apogee). (B) At the point closest to the planet (perigee). (C) The speed is constant throughout the orbit. (D) The speed is greatest when the satellite is moving away from the planet. (E) The speed is greatest when the satellite is moving towards the planet.

What is the SI unit of angular momentum?

(A) kg m/s (B) kg m²/s (C) kg m/s² (D) kg m²/s² (E) N m

Section II: Free Response (3 Questions, 45 Minutes)

Instructions: Answer all three questions. Show your work, including diagrams and equations, where appropriate.

A Block on an Incline: A block of mass m is released from rest at the top of a frictionless inclined plane of height h and angle θ.

(a) Determine the speed of the block at the bottom of the incline.

(b) The inclined plane is now rough, with a coefficient of kinetic friction μk. Derive an expression for the speed of the block at the bottom of the incline in terms of m, g, h, θ, and μk.

(c) If the block comes to rest at the bottom of the incline after traveling a distance d on a horizontal surface with the same coefficient of kinetic friction μk, determine d in terms of h, θ, and μk.
Simple Harmonic Motion: A mass m is attached to a spring with spring constant k and placed on a frictionless horizontal surface. The mass is initially displaced a distance A from its equilibrium position and released from rest.

(a) Derive the equation of motion for the mass.

(b) Determine the period and frequency of the oscillation.

(c) At what position does the mass have its maximum speed? What is the value of the maximum speed?

(d) If a damping force proportional to the velocity (F_d = -bv) is introduced, write the new equation of motion. (Do not solve the differential equation).
Rotational Motion and Conservation of Angular Momentum: A uniform disk of mass M and radius R is rotating with an initial angular velocity ω₀ about a frictionless vertical axle. A small block of mass m is dropped onto the disk at a distance R/2 from the center. The block sticks to the disk.

(a) Calculate the moment of inertia of the disk.

(b) Determine the moment of inertia of the block after it lands on the disk.

(c) Find the final angular velocity of the disk-block system.

(d) Calculate the change in kinetic energy of the system due to the collision. Is kinetic energy conserved? Explain.

Answer Key and Explanations

(Note: These are brief explanations. For a thorough understanding, review the relevant concepts and practice more problems.)

Section I: Multiple Choice

(B) 6 m/s² Explanation: Acceleration is the derivative of velocity with respect to time: a(t) = dv/dt = 6t - 6. At t = 2 s, a(2) = 6(2) - 6 = 6 m/s².
(B) g sin θ Explanation: The component of gravity acting down the incline is mg sin θ. Using Newton's second law, a = (mg sin θ) / m = g sin θ.
(B) (v₀² sin² θ) / (2g) Explanation: At the maximum height, the vertical velocity is zero. Using kinematics, v_f² = v_i² + 2ad, where v_f = 0, v_i = v₀ sin θ, and a = -g. Solving for d (the height), we get (v₀² sin² θ) / (2g).
(A) μk * m * g Explanation: The frictional force is given by f_k = μk * N, where N is the normal force. On a horizontal surface, N = mg. Therefore, f_k = μk * m * g.
(B) Rω Explanation: The linear speed of a point on the rim of a rolling wheel is related to the angular velocity by v = Rω.
(A) (m₁ - m₂) / (m₁ + m₂) * v₁i + (2m₂) / (m₁ + m₂) * v₂i Explanation: This is the standard formula for the final velocity of object 1 in a 1D elastic collision. It's derived from conservation of momentum and kinetic energy.
(A) 2π√(L/g) Explanation: This is the standard formula for the period of a simple pendulum.
(D) (1/2)kx² Explanation: This is the formula for the potential energy stored in a spring.
(C) (1/5)MR²ω² Explanation: Rotational kinetic energy is (1/2)Iω². For a solid sphere, I = (2/5)MR². Therefore, KE_rot = (1/2) * (2/5)MR² * ω² = (1/5)MR²ω².
(D) It decreases by a factor of √2. Explanation: The speed of a satellite in a circular orbit is v = √(GM/r), where G is the gravitational constant, M is the mass of Earth, and r is the radius of the orbit. If r is doubled, v becomes √(GM/2r) = v/√2.
(D) (1/3)ML² Explanation: Use the parallel axis theorem: I = I_center + Md², where d is the distance from the center of mass to the pivot point (L/2). I = (1/12)ML² + M(L/2)² = (1/3)ML².
(C) (3m/2M)v Explanation: Use conservation of momentum: mv + M0 = m*(-v/2) + M*V. Solving for V (the velocity of the block), we get V = (3m/2M)v.
(B) 2αt + β Explanation: Angular velocity is the derivative of angular displacement with respect to time: ω = dθ/dt = 2αt + β.
(A) v²/R Explanation: The centripetal acceleration is given by a_c = v²/R.
(A) 7 J Explanation: Work is the dot product of force and displacement: W = F · Δr = (2i - 3j) · (5i + j) = 2(5) + (-3)(1) = 10 - 3 = 7 J.
(D) Frictional force Explanation: Frictional force is a non-conservative force because the work done by friction depends on the path taken.
(B) There is no frictional force at either the wall or the floor. Explanation: The problem stated smooth wall and floor implying no friction.
(C) (1/4)kx⁴ Explanation: The potential energy function is the negative integral of the force: U(x) = -∫F(x) dx = -∫(-kx³) dx = (1/4)kx⁴ + C. We usually take C = 0.
(C) W/2 Explanation: The tension at the midpoint must support the weight of the cable below the midpoint, which is half the total weight.
(C) Both translational and rotational kinetic energies increase. Explanation: As the yo-yo falls, its potential energy is converted into both translational and rotational kinetic energy.
(A) √(μs * g * r) Explanation: The centripetal force required to keep the block moving in a circle is provided by the static friction force: m*v²/r = μs * m * g. Solving for v, we get v = √(μs * g * r).
(C) It quadruples. Explanation: The total energy of a simple harmonic oscillator is proportional to the square of the amplitude: E = (1/2)kA². If A is doubled, E becomes (1/2)k(2A)² = 4 * (1/2)kA² = 4E.
(D) Moment of inertia Explanation: Moment of inertia (I) is the rotational analog of mass (m) in linear motion.
(C) 50 m Explanation: Use kinematics. Average velocity = (0+20)/2 = 10 m/s. Distance = average velocity * time = 10 * 5 = 50 m. Alternatively, a = (20-0)/5 = 4 m/s². d = v₀t + (1/2)at² = 0 + (1/2)45² = 50 m.
(D) (5/3 i - 1/3 j) Explanation: The position of the center of mass is given by r_cm = (m₁r₁ + m₂r₂) / (m₁ + m₂). r_cm = (m(i + j) + 2m(2i - j)) / (m + 2m) = (5mi - mj) / (3m) = (5/3 i - 1/3 j).
(C) Momentum Explanation: Momentum is always conserved in a closed system. Kinetic energy is only conserved in elastic collisions.
(A) It increases. Explanation: As the person moves towards the center, their moment of inertia decreases. Since angular momentum is conserved (Iω = constant), the angular speed (ω) must increase.
(B) Conservation of momentum Explanation: The rocket pushes exhaust gases backward, and by conservation of momentum, the rocket moves forward.
(D) The negative of the work done by friction. Explanation: Since the block moves at a constant speed, the net work done on it is zero. Therefore, the work done by the applied force F must be equal in magnitude and opposite in sign to the work done by friction.
(D) T√2 Explanation: The period of a simple harmonic oscillator is given by T = 2π√(m/k). If the mass is doubled, the new period is T' = 2π√(2m/k) = T√2.
(C) Impulse Explanation: Impulse is defined as the integral of force over time (J = ∫F dt), which is represented by the area under a force versus time graph.
(A) It is always attractive. Explanation: Gravitational force is always an attractive force between two masses.
(C) (2/3)g Explanation: Using Newton's second law for both linear and rotational motion. The forces are mg - T = ma and the torque is TR = Iα. The moment of inertia of a cylinder is I = (1/2)MR². Also, a = Rα. Solving gives a = (2/3)g.
(B) At the point closest to the planet (perigee). Explanation: By conservation of angular momentum, the speed of the satellite is greatest when it is closest to the planet (perigee) and least when it is farthest from the planet (apogee).
(B) kg m²/s Explanation: Angular momentum (L) is defined as L = r x p, where r is the position vector and p is the linear momentum (p = mv). Therefore, the units of angular momentum are kg * m²/s.

Section II: Free Response

A Block on an Incline:

(a) Speed at the bottom of the frictionless incline: Using conservation of energy: mgh = (1/2)mv². Solving for v, we get v = √(2gh).

(b) Speed at the bottom of the rough incline: The work done by friction is W_f = -μk * m * g * cos θ * (h / sin θ). Using the work-energy theorem: mgh + W_f = (1/2)mv². Solving for v, we get v = √(2gh - 2μk * g * h * cot θ).

(c) Distance d on the horizontal surface: The initial kinetic energy at the bottom of the incline is converted into work done by friction on the horizontal surface: (1/2)mv² = μk * m * g * d. Substituting the expression for v from part (b), we get: (1/2)m(2gh - 2μk * g * h * cot θ) = μk * m * g * d. Solving for d, we get d = h(1 - μk * cot θ) / μk.
Simple Harmonic Motion:

(a) Equation of motion: Using Newton's second law: F = ma = -kx. Therefore, m(d²x/dt²) + kx = 0.

(b) Period and frequency: The angular frequency is ω = √(k/m). The period is T = 2π/ω = 2π√(m/k). The frequency is f = 1/T = (1/2π)√(k/m).

(c) Maximum speed: The mass has its maximum speed at the equilibrium position (x = 0). The maximum speed is v_max = Aω = A√(k/m).

(d) Damped equation of motion: m(d²x/dt²) + b(dx/dt) + kx = 0.
Rotational Motion and Conservation of Angular Momentum:

(a) Moment of inertia of the disk: I_disk = (1/2)MR².

(b) Moment of inertia of the block: I_block = m(R/2)² = (1/4)mR².

(c) Final angular velocity: Using conservation of angular momentum: I_disk * ω₀ = (I_disk + I_block) * ω_f. (1/2)MR² * ω₀ = ((1/2)MR² + (1/4)mR²) * ω_f. Solving for ω_f, we get ω_f = (2Mω₀) / (2M + m).

(d) Change in kinetic energy: Initial kinetic energy: KE_i = (1/2)I_disk * ω₀² = (1/4)MR²ω₀². Final kinetic energy: KE_f = (1/2)(I_disk + I_block) * ω_f² = (1/2)((1/2)MR² + (1/4)mR²) * ((2Mω₀) / (2M + m))². ΔKE = KE_f - KE_i = (M²MR²ω₀² / (2M+m)) - (1/4)MR²ω₀². Kinetic energy is not conserved. The collision is inelastic because the block sticks to the disk, and some energy is lost as heat and sound.

Tips for Success

Master the Fundamentals: Ensure a strong understanding of core concepts such as kinematics, Newton's laws, work-energy theorem, conservation laws, rotational motion, and simple harmonic motion.
Practice Regularly: Consistent practice is crucial. Work through numerous problems from textbooks, past AP exams, and online resources.
Understand the Exam Format: Familiarize yourself with the structure of the AP Physics C: Mechanics exam, including the number of multiple-choice questions and free-response questions, as well as the time allotted for each section.
Review Key Equations: Create a formula sheet with important equations and concepts. While a formula sheet is provided during the exam, knowing the equations well will save you time.
Develop Problem-Solving Skills: Focus on developing a systematic approach to problem-solving. This includes identifying relevant concepts, drawing free-body diagrams, applying appropriate equations, and checking your answers.
Manage Your Time Effectively: Practice pacing yourself during practice exams to ensure you can complete all the questions within the allotted time.
Review Past Exams: Analyze past AP Physics C: Mechanics exams to identify common topics and question types. Pay attention to the scoring guidelines for free-response questions.
Seek Help When Needed: Don't hesitate to ask your teacher, classmates, or online forums for help when you encounter difficult concepts or problems.
Stay Organized: Keep your notes, practice problems, and formula sheets organized for easy reference.
Stay Calm and Confident: On exam day, stay calm and confident. Trust in your preparation and remember that you have the knowledge and skills to succeed.

By consistently practicing and refining your problem-solving skills, you can increase your confidence and achieve a high score on the AP Physics C: Mechanics exam. Good luck!

Ap Physics C Mechanics Practice Exam 2025

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