AP Physics 1: Algebra-Based Practice Quiz: Conservation of Linear Momentum

Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026

Test your understanding with short quizzes. This quiz has 16 questions to check your progress.

Question 1 of 16

Under which of the following conditions is the total momentum of a selected system guaranteed to be constant?

A)When the net internal force on the system is zero.B)When the net external force on the system is zero.C)When the system's kinetic energy is constant.D)When the system is accelerating.

All Questions (16)

Under which of the following conditions is the total momentum of a selected system guaranteed to be constant?

A) When the net internal force on the system is zero.

B) When the net external force on the system is zero.

C) When the system's kinetic energy is constant.

D) When the system is accelerating.

Correct Answer: B

According to the provided content, 'If the net external force on the selected system is zero, the total momentum of the system is constant.' Internal forces do not affect the total momentum of the system.

A system consists of two objects, Object 1 and Object 2. How is the total momentum of this system determined?

A) By the momentum of the more massive object only.

B) By the average of the momenta of the two objects.

C) By the sum of the momenta of the two individual objects.

D) By the difference between the momenta of the two objects.

Correct Answer: C

The provided content states, 'The total momentum of a system is the sum of the momenta of the system's constituent parts.' Therefore, you must add the individual momenta of Object 1 and Object 2 to find the total.

An isolated system is initially at rest. An internal explosion causes the system to break into two pieces that move apart. What can be said about the velocity of the system's center of mass after the explosion?

A) It increases in the direction of the more massive piece.

B) It is equal to the velocity of the faster piece.

C) It remains zero.

D) It is non-zero but constant.

Correct Answer: C

The explosion is an internal force. Since the system is isolated, there is no net external force. The content states, 'The velocity of a system's center of mass is constant in the absence of a net external force.' Since the system was initially at rest, the velocity of the center of mass was zero and must remain zero.

Two skaters, initially at rest on frictionless ice, push off from each other. Skater A moves to the left. What must be true about the momentum of Skater B?

A) The momentum of Skater B is zero.

B) The momentum of Skater B is equal in magnitude and in the same direction as Skater A's momentum.

C) The momentum of Skater B is less in magnitude than Skater A's momentum.

D) The momentum of Skater B is equal in magnitude and opposite in direction to Skater A's momentum.

Correct Answer: D

The two skaters form a system with no net external force (frictionless ice). The push is an internal force. The content states, 'any change to the momentum of an object within a system must be balanced by an equivalent and opposite change of momentum elsewhere within the system.' Since Skater A gained momentum to the left, Skater B must have gained an equal and opposite momentum to the right.

A student drops a ball. If the 'system' is defined as only the ball, why is the momentum of this system not conserved as it falls?

A) Because the ball's mass changes as it falls.

B) Because there is a net external force (gravity) acting on the ball.

C) Because internal forces within the ball cause it to accelerate.

D) Because momentum is only conserved during collisions, not during free fall.

Correct Answer: B

The content explains, 'Describe how the selection of a system determines whether the momentum of that system changes.' and 'If the net external force on the selected system is zero, the total momentum of the system is constant.' When the system is just the ball, the gravitational pull from the Earth is an external force, causing the ball's momentum to change.

A collection of interacting particles is moving through space. Which concept allows this collection to be described as a single entity with a specific velocity?

A) The principle of inertia.

B) The conservation of kinetic energy.

C) The system's center-of-mass velocity.

D) The sum of the internal forces.

Correct Answer: C

The provided content states, 'A collection of objects with individual momenta can be described as one system with one center-of-mass velocity.' This concept simplifies the description of a complex system's overall motion.

A rocket in deep space, far from any significant gravitational forces, expels hot gas out of its engine. The rocket's speed increases. Which statement best describes this situation using the principle of conservation of linear momentum?

A) The force of the gas on the rocket is external, so momentum is not conserved.

B) The rocket and the expelled gas form a system. The forward momentum gained by the rocket is balanced by the backward momentum of the gas, keeping the total momentum of the system constant.

C) Momentum is not conserved because the rocket's mass is decreasing.

D) The velocity of the system's center of mass increases as the rocket accelerates.

Correct Answer: B

This scenario describes the behavior of a system using conservation of linear momentum. By defining the system as the rocket plus its fuel (which becomes the expelled gas), there are no net external forces. The force between the rocket and gas is internal. The change in the rocket's momentum is balanced by an 'equivalent and opposite change of momentum' in the expelled gas, so the total momentum of the rocket-gas system remains constant.

According to the provided principles, which statement is universally true for all interactions within an isolated system?

A) Kinetic energy is conserved.

B) Potential energy is conserved.

C) Momentum is conserved.

D) Velocity is conserved.

Correct Answer: C

The content explicitly states, 'Momentum is conserved in all interactions.' Within the context of an isolated system where net external forces are zero, this principle holds true, whereas kinetic energy is not always conserved (e.g., in inelastic collisions).

A cannon fires a cannonball horizontally. If one wishes to analyze this event using the conservation of linear momentum, which of the following is the most appropriate choice for the 'system'?

A) The cannonball only, because it is the object with the most motion.

B) The cannon only, because it recoils.

C) The cannon and the cannonball together.

D) The cannon, the cannonball, and the Earth.

Correct Answer: C

The selection of the system is crucial. The force that the cannon exerts on the cannonball is equal and opposite to the force the cannonball exerts on the cannon. These are internal forces if the system is defined as the cannon and cannonball together. This choice minimizes the effect of net external forces (like friction, if ignored), allowing momentum to be considered conserved for the system during the brief explosion.

In the absence of a net external force, what is the relationship between the total momentum of a system and the velocity of its center of mass?

A) Both must be zero.

B) Both are constant.

C) The total momentum is constant, but the center-of-mass velocity can change.

D) The center-of-mass velocity is constant, but the total momentum can change.

Correct Answer: B

The content provides two related rules for a system with no net external force: 'the total momentum of the system is constant' and 'The velocity of a system's center of mass is constant'. Both quantities are conserved under this condition.

A system consists of two carts on a frictionless track. Cart 1, moving right, collides with Cart 2, which is stationary. After the collision, Cart 1's momentum has decreased. What must be true about the momentum of Cart 2?

A) It must also decrease to conserve total momentum.

B) It must be zero, as it was initially.

C) It must increase by an amount equal to the momentum lost by Cart 1.

D) It must be greater than the initial momentum of Cart 1.

Correct Answer: C

The system of two carts has no net external force. The content states that 'any change to the momentum of an object within a system must be balanced by an equivalent and opposite change of momentum elsewhere within the system.' Since the total momentum must be constant, the momentum lost by Cart 1 must be gained by Cart 2.

The principle of conservation of linear momentum is a direct consequence of which condition?

A) The absence of internal forces.

B) The presence of a constant velocity.

C) The absence of a net external force.

D) The conservation of mechanical energy.

Correct Answer: C

The content repeatedly emphasizes the core condition for momentum conservation: 'If the net external force on the selected system is zero, the total momentum of the system is constant.' The other options are either incorrect or not the fundamental requirement.

A firecracker is thrown into the air and explodes at the peak of its trajectory. If air resistance is negligible, what happens to the center of mass of the firecracker fragments immediately after the explosion?

A) It drops straight down as the fragments spread out.

B) It continues to follow the original parabolic path it would have taken if it had not exploded.

C) It stops momentarily at the peak and then the fragments fall.

D) It is propelled upward by the force of the explosion.

Correct Answer: B

The explosion consists of internal forces, which do not change the motion of the system's center of mass. The only external force is gravity. The content states that the velocity of the center of mass is constant in the absence of a net external force. With gravity as the external force, the center of mass must follow the same trajectory as any projectile. Therefore, it continues along the parabolic path.

A system is composed of three balls with momenta p1, p2, and p3. The total momentum of the system, P_total, is given by:

A) P_total = p1 + p2 + p3

B) P_total = (p1 + p2 + p3) / 3

C) P_total = p1

D) P_total = 0

Correct Answer: A

This is a direct application of the principle that 'The total momentum of a system is the sum of the momenta of the system's constituent parts.' The total momentum is the vector sum of the individual momenta.

A student stands on a skateboard at rest. The student then throws a heavy ball forward. The skateboard and student move backward. If the system is defined as the student, skateboard, and ball, which statement is the most accurate description of the system's momentum?

A) The total momentum of the system increases because the student does work.

B) The total momentum of the system is not conserved because the ball and student move in opposite directions.

C) The total momentum of the system remains zero because the forward momentum of the ball is balanced by the backward momentum of the student and skateboard.

D) The momentum of the student and skateboard is greater than the momentum of the ball.

Correct Answer: C

The system (student, skateboard, ball) starts with zero total momentum. The act of throwing the ball is an internal force. In the absence of net external forces (like friction), the total momentum must remain constant. Therefore, the initial momentum of zero must be maintained. This is achieved because the forward momentum gained by the ball is equal and opposite to the backward momentum gained by the student and skateboard, as described by the principle that internal momentum changes must be 'equivalent and opposite'.

Consider a collision between a small car and a large truck. During the collision, the force the truck exerts on the car is equal and opposite to the force the car exerts on the truck. Why is the change in the car's momentum much larger than the change in the truck's momentum if the system is defined as only the car?

A) This premise is flawed; the change in the car's momentum is equal and opposite to the change in the truck's momentum.

B) Because the truck has more mass, its inertia resists changes in momentum more effectively.

C) Because the force from the truck is an external force on the car-only system, causing its momentum to change significantly.

D) Because momentum is not conserved in collisions involving objects of very different masses.

Correct Answer: C

This question tests the understanding of system selection. If the system is defined as *only the car*, the force from the truck is a large net external force, which causes a large change in the car's momentum. The statement that the car's change in momentum is larger is based on this flawed system definition. As stated in option A (the key distractor), if the system is the car AND truck, their momentum changes are equal and opposite. However, the question specifically asks why the change is large for the *car-only system*, and the answer is the presence of a net external force, as described by the content: 'the selection of a system determines whether the momentum of that system changes.'