Skip to content
Marlbridge
Free trial

Flashcards · AP® Physics C: Mechanics · Unit 4

Unit 4: Linear Momentum flashcards

32 cards on topics 4.1 to 4.4. Pick a topic or study the whole unit.

Study mode needs JavaScript. Every card is listed below, so you can still cover the answers and test yourself.

All 32 cards

For a quick read-through or printing. Cover the right-hand side to test yourself.

4.1 Linear Momentum

What is linear momentum?
p = mv, a vector in the direction of the velocity, measured in kg·m/s (the same as N·s). In one dimension p_x has the sign of v_x; in two dimensions work with p_x = mv_x and p_y = mv_y.
How do you find the momentum of a system?
Add the momenta of the parts as vectors, by components with signs: p_sys = p₁ + p₂ + …. Opposite momenta cancel, so zero total momentum does not mean everything is at rest.
How are momentum and kinetic energy related?
K = p²/(2m) and |p| = √(2mK). For the same momentum, the lighter object has more kinetic energy. Doubling the speed doubles p but quadruples K.
How do you find momentum from a position function?
p_x(t) = m dx/dt for constant mass. The p–t graph is the v–t graph scaled by m.
What is a collision in the momentum model?
An interaction in which the forces between the objects are much larger than the net external force, so only the states just before and just after are compared and each body can be modelled as an object.
What is an explosion in the momentum model?
An interaction in which internal forces push parts of a system apart. Like a collision, the states just before and just after are compared.
When should you not use the collision model?
When external forces act for a long time compared with the interaction, so their impulse is no longer negligible.
Does momentum depend on the reference frame?
Yes. Momentum depends on velocity, so observers in different inertial frames measure different momenta. Use one frame for the whole problem.

4.2 Change in Momentum and Impulse

How is net force related to momentum?
F_net = dp/dt: the net external force on a system equals the rate of change of its momentum. It is the slope of the p–t graph. For constant mass this reduces to F_net = ma.
What is impulse?
J = ∫F dt, a vector in N·s pointing along the force. It is the signed area under the force–time graph.
What does the impulse–momentum theorem state?
The impulse of the net external force equals the change in momentum: J_net = Δp = p_f − p_i. In two dimensions, apply it to each component separately.
How do you find average force from impulse?
F_avg = J/Δt. For a smooth force pulse, the average force is less than the peak force.
Why does a rebound give a larger impulse than a stop?
Δp uses signed velocities. A 0.30 kg ball hitting a wall at 6.0 m/s and rebounding at 4.0 m/s has Δp = 0.30 × (−4.0 − 6.0) = −3.0 N·s, larger than the 1.8 N·s to stop it.
What force is needed to keep a belt moving at constant speed while mass is added?
F_net = v dm/dt, because the added mass arrives with no momentum along v. Sand falling at 0.50 kg/s onto a belt at 3.0 m/s needs 1.5 N. F = ma does not apply to a system gaining mass.
Which direction does impulse point?
Along the net force, not necessarily along the motion.
When can one force's impulse be taken as Δp?
Only when the other forces are negligible over the interaction, such as weight during a short impact. Check this with numbers.

4.3 Conservation of Linear Momentum

How is total momentum related to center-of-mass velocity?
P = Σmᵢvᵢ = Mv_cm, so v_cm = Σmᵢvᵢ / Σmᵢ = P/M. The whole system can be treated as one object of mass M moving at v_cm.
When is the momentum of a system conserved?
Momentum is conserved in every interaction, but a chosen system keeps constant total momentum only if the net external force on it is zero: dP/dt = ΣF_ext.
Why do internal forces not change a system's total momentum?
By Newton's third law the impulses between parts are equal and opposite, J_on A = −J_on B, so they cancel in the total.
Can momentum be conserved in one direction only?
Yes. If ΣF_ext,x = 0 then P_x is conserved even if a vertical external force acts. A ball dropped vertically into a rolling cart conserves P_x only.
Why can momentum conservation be used across a collision even with gravity acting?
External impulses are tiny over the short contact time, so total momentum just before equals total momentum just after. External forces matter again afterwards.
Does an explosion change the center-of-mass velocity?
No. The forces of an explosion are internal, so v_cm is unchanged if no external force acts.
How is change in system momentum related to external forces?
ΔP = ∫ΣF_ext dt = J_ext, the external impulse transferred from outside the system.
Two skaters at rest push apart. The 70 kg skater moves at +0.60 m/s. What is the 50 kg skater's velocity?
Total momentum stays zero: 70 × 0.60 + 50v = 0, so v = −0.84 m/s.

4.4 Elastic and Inelastic Collisions

What is an elastic collision?
One in which total kinetic energy after equals total kinetic energy before. Momentum is also conserved. Individual kinetic energies can change.
What is an inelastic collision?
One in which total kinetic energy decreases, transformed by nonconservative contact forces into internal energy, sound and permanent deformation. Momentum is still conserved.
What is a perfectly inelastic collision?
The objects stick together and share one velocity v = (m₁u₁ + m₂u₂)/(m₁ + m₂) = v_cm. This is the largest kinetic energy loss momentum allows; K_after = P²/(2M).
What is the shortcut for a one-dimensional elastic collision?
The relative velocity reverses: v₂ − v₁ = −(u₂ − u₁). Use it with momentum conservation instead of the quadratic energy equation.
What are the final velocities for a 1D elastic collision with object 2 at rest?
v₁ = (m₁ − m₂)u₁/(m₁ + m₂) and v₂ = 2m₁u₁/(m₁ + m₂). Equal masses swap velocities.
Is momentum lost in an inelastic collision?
No. Momentum is conserved in every collision of an isolated system. Only kinetic energy decreases.
Can you use energy conservation across an inelastic collision?
No. Use momentum conservation across the collision, then energy conservation for any motion before or after it, such as a ballistic pendulum swinging up.
Does sticking together mean the objects stop?
Only if the total momentum was zero. Otherwise they move off together at v_cm.

Study Unit 4 further

AP® and Advanced Placement® are trademarks registered by the College Board, which is not affiliated with, and does not endorse, this website. Marlbridge is an independent tuition provider. It is not an authorized AP course provider, an AP school or an exam centre, and these resources are not official College Board materials. Reading them or doing simulations does not meet the laboratory requirement of an AP science course.