Lesson 7 – Momentum & Collisions

Stage 1: Intermediate Complete Notes
Page 7 – Two-Dimensional Collisions

In real life, most collisions do not occur along a straight line. When motion before or after collision has components in more than one direction, the collision is called a two-dimensional collision.

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1️⃣ What is a Two-Dimensional Collision?

A collision is said to be two-dimensional when:

• Velocities before or after collision are not along the same line
• Motion occurs in a plane (x-y plane)

✔ Momentum must be conserved in each perpendicular direction

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2️⃣ Conservation of Momentum in Two Dimensions

In two-dimensional collisions, momentum conservation is applied separately along each axis.

Along x-direction: Σp_{x (before)} = Σp_{x (after)}

Along y-direction: Σp_{y (before)} = Σp_{y (after)}

This is because momentum is a vector quantity.

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3️⃣ Typical Example: Oblique Collision

Consider a moving ball striking a stationary ball at an angle.

• Initial momentum exists only in one direction
• After collision, both balls move in different directions

👉 Momentum before collision = Vector sum of momenta after collision

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4️⃣ Elastic Two-Dimensional Collision

In an elastic two-dimensional collision:

✔ Momentum conserved in x-direction
✔ Momentum conserved in y-direction
✔ Kinetic energy conserved

Such collisions are commonly seen in:

• Billiard balls
• Gas molecule collisions

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5️⃣ Inelastic Two-Dimensional Collision

In inelastic two-dimensional collisions:

✔ Momentum conserved in all directions
❌ Kinetic energy not conserved
✔ Direction of motion changes

Example:

• A ball striking another ball and sticking together
• Car collisions at road junctions

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6️⃣ Angle of Scattering (Qualitative)

After collision, bodies move at certain angles with respect to original direction of motion.

✔ These angles depend on masses and initial velocity
✔ Found using momentum components

Detailed numerical problems will be studied at advanced level.

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7️⃣ Important Exam Points

✔ Resolve momentum into components before applying conservation
✔ Apply momentum law separately along each axis
✔ Energy conservation depends on type of collision

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📌 Page 7 Summary

✔ Two-dimensional collision involves motion in a plane
✔ Momentum conserved along each direction
✔ Vector analysis is essential
✔ Forms base for IIT-level problems

👉 Next page: Applications of Momentum Conservation (Recoil, Explosions)