Momentum
56 flashcards covering Momentum for the MCAT Chem / Phys / Psych / Soc section.
Momentum is a fundamental concept in physics that describes the quantity of motion an object possesses. It's calculated as the product of an object's mass and its velocity, so a heavy truck moving slowly might have the same momentum as a light car speeding along. This property helps explain how objects interact during collisions, explosions, or even everyday activities like catching a ball. Understanding momentum is key because it leads to the principle of conservation of momentum, which states that in a closed system, total momentum remains constant unless external forces act on it, making it essential for analyzing real-world dynamics.
On the MCAT, momentum typically appears in the Chemical and Physical Foundations section, often through questions on collisions, impulse, or conservation laws. You'll encounter multiple-choice problems requiring you to calculate momentum, determine outcomes of elastic versus inelastic collisions, or apply vector principles. Common traps include confusing momentum with kinetic energy, overlooking direction in vector problems, or misapplying formulas in complex scenarios. Focus on mastering problem-solving techniques, visualizing interactions, and practicing with diagrams to handle these questions efficiently.
A concrete tip: Always check units and directions when solving momentum problems.
Terms (56)
- 01
Momentum
Momentum is a vector quantity that measures an object's motion, defined as the product of its mass and velocity.
- 02
Formula for momentum
The formula for momentum is p = m × v, where p is the momentum, m is the mass of the object, and v is its velocity.
- 03
Units of momentum
The SI unit of momentum is kilogram meters per second (kg·m/s), derived from multiplying mass in kilograms by velocity in meters per second.
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Vector nature of momentum
Momentum is a vector, meaning it has both magnitude and direction, and changes in direction affect the momentum even if speed remains constant.
- 05
Impulse
Impulse is the product of the net force acting on an object and the time duration of that force, resulting in a change in the object's momentum.
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Impulse-momentum theorem
The impulse-momentum theorem states that the impulse applied to an object equals the change in its momentum, expressed as J = Δp.
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Conservation of momentum
In a closed system with no external forces, the total momentum of the system remains constant before and after an event, such as a collision.
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Elastic collision
An elastic collision is one where both kinetic energy and momentum are conserved, meaning the objects bounce off each other without losing mechanical energy.
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Inelastic collision
An inelastic collision is one where momentum is conserved, but kinetic energy is not, often resulting in deformation or heat generation.
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Perfectly inelastic collision
A perfectly inelastic collision occurs when two objects stick together after colliding, conserving momentum but losing the maximum possible kinetic energy.
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Coefficient of restitution
The coefficient of restitution measures the elasticity of a collision, defined as the relative speed of separation divided by the relative speed of approach, ranging from 0 to 1.
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Center of mass
The center of mass is the point in a system where the system's total mass can be considered concentrated, and it moves as if all external forces act at that point.
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Momentum in explosions
In an explosion, the total momentum of the system is conserved if no external forces act, meaning the vector sum of the momenta of the fragments equals the initial momentum.
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Two-dimensional collisions
In two-dimensional collisions, momentum is conserved in both the x and y directions separately, requiring vector components to be analyzed.
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Change in momentum
Change in momentum is calculated as the difference between final and initial momentum vectors, often used to determine forces or impulses.
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Momentum of a system
The total momentum of a system is the vector sum of the individual momenta of all objects within it, which remains constant in isolated systems.
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External forces and momentum
External forces can change the total momentum of a system, while internal forces do not, as they cancel out in pairs according to Newton's third law.
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Kinetic energy vs. momentum
Unlike kinetic energy, which is scalar and depends on speed squared, momentum is a vector that depends on both mass and velocity direction.
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Common trap: Mass and velocity confusion
A common error is confusing momentum with mass or velocity alone; momentum requires both, and increasing mass or velocity increases momentum proportionally.
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Strategy for collision problems
To solve collision problems, first identify if the system is isolated, then apply conservation of momentum in each direction, and check for kinetic energy conservation.
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Momentum in variable mass systems
In systems with variable mass, like rockets, momentum conservation requires considering the ejected mass, as the system's mass changes over time.
- 22
Relativistic momentum
Although MCAT focuses on classical physics, relativistic momentum is p = γ m v, where γ is the Lorentz factor, but this is rarely tested.
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Example of elastic collision calculation
For two objects colliding elastically, solve by conserving both momentum and kinetic energy; for instance, a 2 kg object at 3 m/s hits a stationary 1 kg object, resulting in specific final velocities.
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Momentum conservation in everyday life
Momentum conservation explains phenomena like a person jumping off a boat, where the boat moves backward to conserve the system's total momentum.
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Angular momentum
Angular momentum is the rotational equivalent of linear momentum, given by L = I ω, where I is moment of inertia and ω is angular velocity, conserved in rotating systems.
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Torque and angular momentum
Torque is the rotational equivalent of force, changing angular momentum over time, similar to how force changes linear momentum.
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Precession and angular momentum
Precession occurs when a spinning object like a gyroscope maintains its angular momentum direction while its axis rotates around another axis.
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Conservation of angular momentum
In a system with no external torques, angular momentum is conserved, meaning it remains constant in both magnitude and direction.
- 29
Figure skater spin example
A figure skater spins faster when pulling in their arms because conserving angular momentum decreases moment of inertia, increasing angular velocity.
- 30
Linear momentum in fluids
In fluid dynamics, linear momentum principles apply to concepts like Bernoulli's equation, where momentum changes relate to pressure differences.
- 31
Impulse from a force-time graph
The impulse can be found from a force-time graph as the area under the curve, which equals the change in momentum of the object.
- 32
Average force and impulse
Average force is impulse divided by the time interval, allowing calculation of forces in collisions when momentum change is known.
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Momentum and Newton's second law
Newton's second law can be expressed as F = dp/dt, meaning net force equals the rate of change of momentum, not just mass times acceleration if mass varies.
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Common trap: Direction in vectors
Forgetting that momentum is a vector can lead to errors in problems with angles; always resolve into components for accuracy.
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Worked example: Car collision
In a head-on collision, if a 1000 kg car at 20 m/s hits a 1500 kg car at 10 m/s, conservation of momentum gives the final velocities after impact.
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Momentum in projectile motion
In projectile motion, the horizontal component of momentum remains constant due to no horizontal forces, while vertical momentum changes with gravity.
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System isolation for momentum
To apply momentum conservation, define the system such that no external forces act on it, or their effects are negligible over the time frame.
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Inelastic collision energy loss
In inelastic collisions, the lost kinetic energy converts to other forms like sound or heat, but the total energy is still conserved.
- 39
Strategy for elastic collision equations
For elastic collisions, set up equations for conservation of momentum and kinetic energy, then solve the system of equations for unknowns.
- 40
Momentum of photons
Photons have momentum p = h/λ, where h is Planck's constant and λ is wavelength, relevant in quantum physics contexts on the MCAT.
- 41
Common trap: Assuming equal masses
In collision problems, do not assume final velocities are equal unless masses are equal and it's a head-on elastic collision; always calculate.
- 42
Center of mass velocity
The velocity of the center of mass of a system equals the total momentum divided by the total mass, remaining constant if no external forces act.
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Momentum in circular motion
In uniform circular motion, linear momentum changes direction constantly, requiring a centripetal force to maintain the path.
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Example: Billiard balls collision
When a moving billiard ball strikes a stationary one of equal mass elastically, the first stops, and the second moves with the initial velocity of the first.
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Impulse units
The units of impulse are newton-seconds (N·s), which are equivalent to kg·m/s, the same as momentum, since impulse equals change in momentum.
- 46
Variable force impulse
For a variable force, impulse is the integral of force with respect to time, equating to the total change in momentum.
- 47
Momentum conservation exceptions
Momentum is not conserved if external forces like friction act on the system; identify and account for them in real-world problems.
- 48
Angular momentum vector
Angular momentum is a vector perpendicular to the plane of rotation, with its direction given by the right-hand rule.
- 49
Gyroscope stability
A gyroscope's angular momentum keeps it stable against tipping due to the conservation of angular momentum in the absence of torques.
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Worked example: Rocket launch
In a rocket launch, conservation of momentum explains how the rocket gains velocity as it ejects mass backward at high speed.
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Momentum and inertia
While inertia relates to mass resisting acceleration, momentum incorporates both mass and velocity, making it a dynamic measure.
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Two-body problem in collisions
For two isolated bodies colliding, the equations of conservation of momentum and energy can fully determine their post-collision states.
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Common trap: Kinetic energy conservation
Do not assume kinetic energy is conserved in all collisions; only elastic ones preserve it, while inelastic ones do not.
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Momentum in waves
In wave mechanics, particles like electrons have wave-like momentum, but this is more advanced and relates to quantum concepts on the MCAT.
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Strategy for multi-object systems
For systems with multiple objects, calculate total initial and final momentum by summing vectors, ensuring conservation holds.
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Example: Bullet and block
A bullet embedding in a block is a perfectly inelastic collision, where momentum conservation finds the final velocity of the combined mass.