Calculator Inputs
Formula Used
This calculator splits each velocity into normal and tangential components. The normal direction follows the line of impact. The tangential direction is perpendicular to it.
| Step | Formula | Meaning |
|---|---|---|
| Vector components | vx = v cos θ, vy = v sin θ |
Converts speed and angle into x and y velocity. |
| Normal velocity | uₙ = v · n |
Projects velocity on the collision normal. |
| Tangential velocity | uₜ = v · t |
Projects velocity on the tangent line. |
| Body 1 after impact | v₁ₙ = ((m₁-m₂)/(m₁+m₂))u₁ₙ + (2m₂/(m₁+m₂))u₂ₙ |
Finds the final normal component of body 1. |
| Body 2 after impact | v₂ₙ = (2m₁/(m₁+m₂))u₁ₙ + ((m₂-m₁)/(m₁+m₂))u₂ₙ |
Finds the final normal component of body 2. |
| Final angle | θ = atan2(vy, vx) |
Returns each body direction after collision. |
How to Use This Calculator
- Enter the mass of each object in kilograms.
- Enter the starting speed for each object.
- Enter each starting direction in degrees.
- Set the collision normal angle. This is the line of impact.
- Choose the number of decimal places.
- Press the calculate button.
- Read the final speed, final angle, and deflection angle.
- Use the CSV or PDF button to save the results.
Example Data Table
| Example | m1 kg | m2 kg | v1 m/s | θ1 | v2 m/s | θ2 | Normal angle | Use case |
|---|---|---|---|---|---|---|---|---|
| Equal masses | 1 | 1 | 10 | 0° | 0 | 0° | 45° | Billiard ball style impact |
| Heavy target | 1 | 5 | 12 | 10° | 0 | 0° | 25° | Projectile hits larger object |
| Moving bodies | 2 | 3 | 8 | 0° | 4 | 180° | 15° | Two objects meet at an angle |
| Glancing hit | 4 | 2 | 9 | 20° | 1 | 90° | 70° | Small contact deflection |
Elastic Collision Angle Guide
What the Angle Means
An elastic collision angle describes the direction of each object after impact. It is useful when two bodies collide in a plane. The objects may be balls, particles, carts, or ideal point masses. In a perfect elastic collision, total kinetic energy stays the same. Total momentum also stays the same. These two conservation rules make the final motion predictable.
Why Vector Components Matter
A two dimensional collision is easier when velocity is split into parts. One part acts along the collision normal. The other part acts along the tangent. Only the normal parts exchange motion during a smooth elastic impact. The tangential parts remain unchanged. This method gives clean results for angled hits. It also avoids guessing the final direction.
Practical Physics Use
This calculator helps students test collision examples quickly. It also helps teachers prepare classroom demonstrations. Engineers can use it for simple impact studies. Game developers can compare collision response behavior. The graph makes the direction change easier to see. The result table shows speed, angle, energy, and momentum checks.
Interpreting the Output
Start with the final angle values. These show where each body moves after impact. Next, check the deflection values. A positive value means the object turned counterclockwise. A negative value means it turned clockwise. Then review the energy and momentum errors. Small errors show that the calculation is consistent. Large errors usually mean an input was unrealistic.
Best Input Practice
Use SI units for simple reading. Keep masses positive. Use zero speed for a stationary target. Choose the normal angle carefully. It should match the contact line between the two centers. For round balls, this line joins both centers at impact. Correct geometry gives better final angles.
FAQs
What is an elastic collision angle?
It is the final movement direction of an object after an elastic impact. The angle is measured from the positive x-axis in this calculator.
Does this calculator conserve kinetic energy?
Yes. It models a perfectly elastic collision. It also displays energy before and after the collision so you can compare both values.
What is the collision normal angle?
It is the direction of the line of impact. For round objects, it is the line joining both centers at the collision moment.
Can I use this for a stationary target?
Yes. Enter zero for the second object speed. Keep its angle at any value, because zero speed has no direction effect.
Why are tangential components unchanged?
For a smooth ideal elastic impact, impulse acts along the normal direction. No tangential impulse is applied, so tangential velocity remains unchanged.
What does deflection angle show?
It shows how much the object direction changed. Positive values mean counterclockwise turning. Negative values mean clockwise turning.
Can this handle two moving objects?
Yes. Enter the speed and direction for both objects. The calculator uses both initial velocity vectors in the final result.
Why do results show tiny energy errors?
Tiny differences can appear because computers use rounded decimal arithmetic. Very small errors are normal and usually harmless.