Momentum is the vector quantity $\vec{p}=m\vec{v}$. Its magnitude depends on mass and speed, and its direction is the direction of velocity.

What does it mean to resolve momentum into components?

It means expressing the momentum vector as portions along perpendicular coordinate axes, such as $p_x$ and $p_y$.

How is momentum conserved in two dimensions?

For a closed system, total momentum is conserved independently along each axis: initial and final $x$-components match, and initial and final $y$-components match.

Why does a collision problem need a closed-system assumption?

Momentum conservation applies when the net external impulse on the chosen system is zero or negligible during the interval being considered.

How do you find a vector's magnitude from its perpendicular components?

Use the Pythagorean theorem. For velocity, $v=\sqrt{v_x^2+v_y^2}$; the same method applies to momentum components.

Classical mechanicsLesson 5 of 7 in the course Linear Momentum and Collisions

Two-Dimensional Momentum in Collisions and Explosions

5 flashcards · 5 quiz questions · 5 match pairs · 4 fill-in sentences · English

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Summary

In a two-dimensional collision, objects can move in different directions before and after impact. To analyze such motion, we treat momentum as a vector and resolve it into perpendicular components.

Momentum is defined by $\vec{p}=m\vec{v}$ , where mass is a scalar and velocity is a vector. Therefore momentum is also a vector: it has both magnitude and direction. Two momenta pointing in different directions cannot generally be combined by simply adding their magnitudes.

All flashcards

What is momentum?: Momentum is the vector quantity $\vec{p}=m\vec{v}$ . Its magnitude depends on mass and speed, and its direction is the direction of velocity.
What does it mean to resolve momentum into components?: It means expressing the momentum vector as portions along perpendicular coordinate axes, such as $p_x$ and $p_y$ .
How is momentum conserved in two dimensions?: For a closed system, total momentum is conserved independently along each axis: initial and final $x$ -components match, and initial and final $y$ -components match.
Why does a collision problem need a closed-system assumption?: Momentum conservation applies when the net external impulse on the chosen system is zero or negligible during the interval being considered.
How do you find a vector's magnitude from its perpendicular components?: Use the Pythagorean theorem. For velocity, $v=\sqrt{v_x^2+v_y^2}$ ; the same method applies to momentum components.

Quiz questions

An object initially at rest breaks into three fragments in an isolated explosion. How can the momentum of the third fragment be found from the first two?Answer: $\vec{p}_3=-(\vec{p}_1+\vec{p}_2)$
When two objects stick together in an isolated collision, which quantity is conserved but kinetic energy generally is not?Answer: The system's total momentum
Two objects with masses $m_1$ and $m_2$ stick together. Which expression gives their shared final velocity?Answer: $\vec{v}_f=\frac{m_1\vec{v}_{1,i}+m_2\vec{v}_{2,i}}{m_1+m_2}$
A velocity vector has $v_x<0$ and $v_y<0$ . In which quadrant does it point?Answer: Quadrant III
To convert a speed from kilometers per hour to meters per second, what operation should be used?Answer: Divide the numerical value by $3.6$

Based on University Physics Volume 1 by William Moebs, Samuel J. Ling, Jeff Sanny (OpenStax), licensed CC BY 4.0. Adapted into a summary, flashcards and quizzes.

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