Momentum and collisions in two dimensions add complexity to our understanding of motion. We'll explore how momentum behaves as a vector quantity, with components in both x and y directions. This builds on our previous knowledge of one-dimensional motion.
Conservation of momentum applies separately to both x and y components in two-dimensional collisions. We'll analyze elastic and inelastic collisions, using conservation equations to solve problems involving objects moving at angles. This expands our toolkit for understanding real-world interactions.
Momentum and Collisions in Two Dimensions
Momentum as vector quantity
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Top images from around the web for Momentum as vector quantity
9.3 Conservation of Linear Momentum | University Physics Volume 1 View original
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Collisions in Multiple Dimensions – University Physics Volume 1 View original
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Collisions of Extended Bodies in Two Dimensions | Physics View original
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9.3 Conservation of Linear Momentum | University Physics Volume 1 View original
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Collisions in Multiple Dimensions – University Physics Volume 1 View original
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Momentum is a vector quantity has both magnitude and direction
In two dimensions, momentum is represented by a vector with components in the x and y directions
px=mvx where m is mass and vx is velocity in x-direction
py=mvy where vy is velocity in y-direction
is sum of its components p=pxi^+pyj^
i^ and j^ are unit vectors in x and y directions respectively
Magnitude of momentum vector given by ∣p∣=px2+py2
Direction of momentum vector given by angle θ=tan−1(pxpy)
Examples:
Car moving northeast has momentum components in both x and y directions
Billiard ball struck off-center has initial momentum at an angle to the x-axis
Conservation of momentum in components
Law of conservation of momentum states total momentum of closed system remains constant
In two dimensions, both x and y components of total momentum are conserved separately