1. What is Impulse?

Impulse is the change in momentum of an object when a force is applied over a time interval. It is a vector quantity, meaning it has both magnitude and direction. The impulse-momentum theorem states that the impulse on an object is equal to the change in its momentum.

2. How Does the Calculator Work?

The calculator uses the impulse equation:

Where:

• \( \vec{I} \) — Impulse vector (kg·m/s)
• \( m \) — Mass of the object (kg)
• \( \vec{v_f} \) — Final velocity vector (m/s)
• \( \vec{v_i} \) — Initial velocity vector (m/s)

Explanation: The calculator computes the difference between final and initial velocity vectors, then multiplies by mass to get the impulse vector. It also calculates the magnitude of this vector.

3. Importance of Impulse Calculation

Details: Impulse calculations are crucial in physics and engineering, particularly in analyzing collisions, rocket propulsion, sports mechanics, and vehicle safety systems.

4. Using the Calculator

Tips: Enter mass in kilograms and velocity components in meters per second. For 2D problems, set the z-components to zero. All values must be valid (mass > 0).

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between impulse and momentum?
A: Momentum is mass times velocity (p = mv), while impulse is the change in momentum (I = Δp = mΔv).

Q2: How is impulse related to force?
A: Impulse equals force multiplied by time (I = FΔt). This is why airbags reduce impact force by increasing collision time.

Q3: What are typical units for impulse?
A: The SI unit is kg·m/s (same as momentum), or equivalently N·s (newton-seconds).

Q4: Can impulse be negative?
A: Yes, the components can be negative indicating direction opposite to the coordinate axes, but magnitude is always positive.

Q5: How is this different from work?
A: Work is scalar (F·d) while impulse is vector (F·t). Work changes energy, impulse changes momentum.