Momentum Calculator (p = m · v) – Tutorial

Momentum (p = m·v) – Detailed Lesson

Momentum is a fundamental quantity that tells us "how hard it is to stop an object or change its direction of motion." It plays a critical role in collision, impulse, and conservation of momentum problems.

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1) Definition and Formula

p = m · v

• m: mass (kg)
• v: velocity (m/s)
• p: momentum (kg·m/s)

The most important point: velocity is a vector. Therefore momentum also carries direction. When velocity is entered as negative, momentum is also negative — this means "opposite direction."

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2) SI Units

In the SI system:

• m: kg
• v: m/s
• p: kg·m/s

This calculator can also perform the following conversions automatically:

• km/h → m/s: v(m/s) = v(km/h) / 3.6
• g → kg: 1000 g = 1 kg
• ton → kg: 1 ton = 1000 kg

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3) Difference from Kinetic Energy

Momentum and kinetic energy are often confused:

• Momentum carries direction (sign matters).
• Kinetic energy has no direction, it is always ≥ 0.

E_k = 1/2 · m · v²

For the same velocity, increasing mass raises both p and E_k. But note: doubling velocity doubles momentum, but quadruples kinetic energy (because of v²).

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4) Conservation of Momentum (Golden Rule for Collisions)

If external forces can be neglected (or the interaction time is very short), total momentum is conserved:

p_{total, before} = p_{total, after}

This is why in collision problems the "momentum" equation is often more reliable than the "energy" equation.

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5) Connection to Impulse

Impulse equals the change in momentum:

J = Δp

This calculator finds p for a single object. To find the change in momentum (Δp) during a collision, calculate p before and after separately, then subtract.

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6) Common Mistakes

• Entering speed in km/h but treating it as m/s (result is off by a factor of 3.6).
• Entering mass in grams but treating it as kg (factor of 1000 difference).
• Thinking negative velocity means an error — it doesn't; it conveys direction.