Name: momentum transfer in billiard collisions
Uploaded: 2024-03-07T13:22:20.000Z
Duration: 1 min 28 s
Channel: JoVE

K12 Standards

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South Carolina College and Career Ready Science Standards

High School

Physics

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Motion and Stability: Forces and Interactions

P-PS2-2

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Conservation of Linear Momentum for a System of Particles

In a game of billiards, when the cue ball strikes a stationary ball, it transfers some of its momentum to the stationary ball. The cue ball slows down, and the struck ball starts moving.
The impulsive force acting on the ball is for a very short duration. So its impulse can be neglected.
When the sum of external impulses acting on a system of particles is zero, the principle of linear impulse and momentum simplifies, representing the conservation of linear momentum. This principle is commonly applied when particles collide or interact.
In impulse-momentum analysis, forces can be impulsive or non-impulsive.
Impulsive forces act briefly yet cause substantial momentum changes. For instance, the forceful impact of a moving ball on a stationary one in billiards leads to immediate momentum change for both balls.
Conversely, non-impulsive forces operate over longer periods compared to the time of the collision, such as the friction between balls and the table. Though slightly affecting momentum, their impact is minor compared to collision forces.

conservation of linear momentum for a system of particles

In the dynamic realm of billiards, a fascinating interplay of forces governs the motion of cue balls and stationary balls. When the cue ball collides with a stationary ball, linear momentum is exchanged. The cue ball imparts a fraction of its linear momentum to the stationary ball, causing the cue ball to decelerate while initiating the motion of the stationary ball.
The impulsive force at play during this interaction is of extremely short duration, rendering its impulse negligible. When considering a system of particles in motion, the sum of external impulses is of great importance. If this sum equals to zero, the principle of linear impulse and momentum comes into play, elegantly illustrating the conservation of linear momentum. This principle finds widespread application in scenarios involving particle collisions or interactions.
Within impulse-momentum analysis, forces can be categorized as impulsive or non-impulsive. Impulsive forces, despite their brief duration, instigate significant momentum changes. A prime example is the forceful collision between a moving ball and a stationary one in billiards, triggering an instantaneous shift in momentum for both spheres.
Conversely, non-impulsive forces operate over extended periods, surpassing the collision timeframe. These forces, exemplified by friction between balls and the table, subtly influence momentum but pale in comparison to the transformative impact of collision forces.

In a game of billiards, when the cue ball strikes a stationary ball, it transfers some of its momentum to the stationary ball. The cue ball slows down, ...

Education

JoVE Core

Mechanical Engineering

Unit 1

Kinetics of a Particle: Impulse and Momentum

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KEY TERMS AND CONCEPTS

momentum transfer in billiard collisions

Momentum transfer in billiard collisions shows how linear momentum changes when one ball strikes another. A moving cue ball hits a stationary ball and gives up part of its linear momentum. The cue ball slows down, and the other ball starts moving.

The collision force acts for an extremely short time, so its impulse is negligible. In impulse-momentum analysis, forces are grouped as impulsive or non-impulsive. Impulsive forces act briefly but can cause a large momentum change.

For a system of particles, the total external impulse is important. If the sum of external impulses is zero, the linear impulse and momentum principle applies. That result shows conservation of linear momentum for the system.

This idea is useful in many particle collisions and interactions. Friction between the balls and the table is a non-impulsive force, because it acts over a longer time than the collision itself. Its effect on momentum is small compared with the sudden impact between the balls.

Momentum Transfer in Billiard Collisions

principle of linear impulse and momentum for a single particle

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Momentum and Impulse Diagrams for a Particle

Linear momentum describes how a particle moves in physics. It is a vector quantity, so it has both size and direction. Its magnitude equals mass times velocity, and its direction matches the particle’s velocity. Linear impulse, also called momentum impulse, describes the change in linear momentum. It is also a vector quantity. Impulse equals force multiplied by the time interval over which the force acts. For a particle of mass m in an inertial frame, the equation of motion can be integrated...

principle of linear impulse and momentum for a single particle: problem solving

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Solving a Two-Mass Pulley Momentum Problem

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principle of linear impulse and momentum for a system of particles

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Center of Mass and Particle Momentum

A system of particles follows an equation of motion that describes how external forces affect its motion in an inertial frame of reference. The particles also exert internal forces on one another, but these forces act in equal and opposite collinear pairs. Because they cancel, they do not appear in the equation of motion. The principle of linear impulse and momentum comes from integrating that equation of motion over time. After the limits are applied, the combined initial linear momenta of...

Momentum transfer in billiard collisions shows how linear momentum changes when one ball strikes another. A moving cue ball hits a stationary ball and gives up part of its linear momentum. The cue ball slows down, and the other ball starts moving. The collision force acts for an extremely short time, so its impulse is negligible. In impulse-momentum analysis, forces are grouped as impulsive or non-impulsive. Impulsive forces act briefly but can cause a large momentum change. For a system of...

impact

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angular momentum

Angular Momentum and Direction

Angular momentum describes rotational motion and the direction of that motion. It is defined as the moment of a particle’s linear momentum about a chosen point O. This makes it useful for describing how motion curves around a point. For a particle moving along a curved path in the x-y plane, the scalar form gives the magnitude of angular momentum. It uses the moment arm, d, which is the perpendicular distance from point O to the line of action of the linear momentum. Even when written in...

relation between moment of a force and angular momentum

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principle of angular impulse and momentum

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Angular Impulse, Momentum, and Rotation

Angular impulse and momentum describe how forces change an object's rotation over time. The idea connects the moment of force, or torque, with angular momentum. When the equation is integrated from an initial time to a final time, it gives the angular impulse and momentum principle. The principle defines initial and final angular momentum as the moments of a particle's linear momentum at those specific times. Angular impulse is found by integrating the moments of all forces acting on the...

principle of angular impulse and momentum: problem solving

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Angular Impulse and Final Velocity

Angular impulse and momentum help determine the final velocity of a ball attached to a massless rod. The ball has mass m and moves under a time-dependent torque. If the initial velocity is known, the final velocity after a time interval can be found with this principle. The first step is to draw a free-body diagram. A free-body diagram shows all the forces acting on the system. It helps make the motion and rotation easier to analyze. Next, the principle of angular impulse and momentum is...

steady flow of a fluid stream

Fluid Force and Momentum in a Pipe

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key terms and concepts

Explore how a cue ball transfers momentum in a billiard collision, and how impulsive and non-impulsive forces affect a system of particles.

Momentum Transfer in Billiard Collisions | JoVE K12

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Momentum Transfer in Billiard Collisions

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