Calculate Momentum, Mass, or Velocity | p = m × v | Physics Tool
Result
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📝 Step-by-step solution
Select what to calculate and enter values
💡 Momentum p in kg·m/s | Mass m in kg | Velocity v in m/s | 1 kg·m/s = 1 N·s
📖 What is Momentum?
Momentum is a fundamental quantity in physics that describes the "quantity of motion"
of an object. It is the product of an object's mass and its velocity. Momentum is a vector quantity —
it has both magnitude and direction. It plays a central role in Newton's laws of motion and the law of
conservation of momentum.
p = m × v
Where:
• p = Momentum (kg·m/s)
• m = Mass (kg)
• v = Velocity (m/s)
🔁 Rearranged Formulas
Momentum: p = m × v Mass: m = p / v Velocity: v = p / m
📝 Worked Example
Example: Momentum of a 1500 kg Car Moving at 20 m/s
Given: Mass m = 1500 kg | Velocity v = 20 m/s
Formula: p = m × v Calculation: p = 1500 × 20 = 30,000 kg·m/s Result: The car's momentum is 30,000 kg·m/s in the direction of motion.
📊 Real-World Applications
Vehicle Safety: Crumple zones increase collision time, reducing force by spreading out momentum change.
Sports: A heavier or faster ball has more momentum — harder to stop (e.g., cricket, tennis).
Rocket Science: Rocket momentum changes as exhaust gases are ejected in the opposite direction.
Particle Physics: Momentum conservation is used to detect and analyze subatomic particles.
Astronomy: Planets, comets, and galaxies exchange momentum through gravitational interactions.
⚠️ Limitations & Assumptions
📌 Important Notes
Assumes constant mass and velocity — for relativistic speeds (close to light speed), use relativistic momentum.
Velocity is a vector — direction matters. This calculator treats speed as the magnitude.
Not suitable for variable-mass systems (e.g., rockets burning fuel) without extra equations.
For collisions, use conservation of momentum: p₁ + p₂ = p₁' + p₂'.
Results are theoretical estimates — real systems may involve friction, air resistance, or other losses.
📚 References & Sources
Authoritative Sources
OpenStax — University Physics, Volume 1 (Chapter 9: Linear Momentum and Collisions)
NIST — Guide to the SI Units (kg·m/s)
Khan Academy — Momentum and Impulse
Halliday, Resnick, Walker — Fundamentals of Physics
❓ Frequently Asked Questions
What is the difference between momentum and inertia?
Inertia is the resistance of an object to any change in its motion and depends only on mass.
Momentum depends on both mass and velocity — a fast-moving object has more momentum
even if it has the same mass.
Is momentum a vector or scalar quantity?
Momentum is a vector quantity — it has both magnitude and direction.
A car moving east at 20 m/s has opposite momentum to a car moving west at 20 m/s.
How is momentum related to force?
According to Newton's second law, Force = change in momentum / change in time (F = Δp/Δt).
This is why airbags reduce injury — they increase the collision time, reducing the force.
Does momentum depend on the direction of motion?
Yes — momentum is directional. Two objects with the same speed but opposite directions have
equal magnitude but opposite momentum vectors.
Can momentum be negative?
Yes — momentum can be negative if you choose a reference direction. For example, a ball moving
west might have negative momentum if east is defined as positive.
This Momentum Calculator is provided for informational and educational purposes only.
Results are based on standard physics formulas and assumed constant mass and velocity.
Real-world systems may involve relativistic effects, variable mass, or external forces.
Always verify critical calculations with authoritative sources or a qualified physics professional.