Momentum Formula – Definition, Derivation & Solved Examples

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What Is the Momentum Formula?

The momentum formula defines momentum as the product of an object's mass and its velocity:

p = mv

where p is momentum, m is mass (in kg), and v is velocity (in m/s). Since velocity is a vector quantity (it has direction), momentum is also a vector — it always points in the same direction as the object's velocity. This formula for momentum is one of the most frequently used equations in Class 11 Physics, forming the basis for impulse, collisions, and the conservation of momentum.

What Is the SI Unit and Dimensional Formula of Momentum?

How Is the Formula for Momentum Derived from Newton's Second Law?

Newton's second law states that the rate of change of momentum of an object is directly proportional to the net force applied on it, and this change occurs in the direction of the applied force:

F = dp/dt

For a constant mass system, substituting p = mv gives:

F = d(mv)/dt = m(dv/dt) = ma

This shows that the familiar equation F = ma is actually a special case of the more general momentum formula F = dp/dt, which also holds true even when mass changes (such as in rocket propulsion problems).

What Is the Difference Between Linear Momentum and Angular Momentum?

This page focuses on linear momentum, since that is what the standalone "momentum formula" typically refers to in Class 11 Laws of Motion.

What Is the Impulse-Momentum Theorem and How Does It Relate to the Momentum Formula?

The impulse-momentum theorem connects force, time, and momentum change. Impulse (J) is defined as:

J = FΔt = Δp = m(v − u)

where u is the initial velocity and v is the final velocity. This means the impulse delivered to an object equals its change in momentum — a direct consequence of the momentum formula and Newton's second law. This relationship explains everyday physics like why airbags reduce injury (by increasing the time of impact, Δt, they reduce the average force for the same change in momentum). Practice how impulse-momentum questions are asked with JEE Main Chapterwise PYQ.

What Is the Law of Conservation of Momentum?

The law of conservation of momentum states that in the absence of external forces, the total momentum of a closed system remains constant. For a two-body collision:

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

where u₁, u₂ are initial velocities and v₁, v₂ are final velocities of the two bodies. This formula for momentum conservation is one of the most tested concepts in Physics, applied extensively in problems involving elastic and inelastic collisions. Collision-based numericals are a recurring pattern in JEE Advanced Chapterwise PYQ, often combined with energy conservation.

How Do You Solve Problems Using the Momentum Formula? (Solved Examples)

Example 1: Basic momentum calculation. A ball of mass 0.5 kg moves with a velocity of 10 m/s. Find its momentum. Solution: p = mv = 0.5 × 10 = 5 kg·m/s

Example 2: Momentum change using impulse. A cricket ball of mass 0.15 kg moving at 12 m/s is hit back at 20 m/s in the opposite direction. Find the change in momentum. Solution: Δp = m(v − u) = 0.15 × [20 − (−12)] = 0.15 × 32 = 4.8 kg·m/s

Example 3: Conservation of momentum in collision. A 2 kg object moving at 3 m/s collides with a stationary 1 kg object, and they stick together. Find their common velocity after collision. Solution: Using m₁u₁ + m₂u₂ = (m₁ + m₂)v 2(3) + 1(0) = (2+1)v → 6 = 3v → v = 2 m/s

Example 4: Force from rate of change of momentum. A force acting on a 4 kg object changes its velocity from 2 m/s to 10 m/s in 4 seconds. Find the average force. Solution: F = Δp/Δt = m(v−u)/t = 4(10−2)/4 = 4(8)/4 = 8 N

Why Is Understanding the Momentum Formula Important for JEE and NEET?

Momentum-based questions appear consistently in both JEE Main and NEET, not only within Laws of Motion but also embedded in Work-Energy-Power (collisions), System of Particles (center of mass and angular momentum), and even Rotational Motion. A clear grasp of the momentum formula, impulse-momentum theorem, and conservation of momentum is essential, since these concepts are rarely tested in isolation and often combined with energy conservation in multi-step numerical problems. Test this exact combination with NEET Chapterwise PYQ, since momentum-energy questions appear regularly in NEET Physics too.

How Should Students Practice Momentum Formula Problems?

1. Start with direct substitution problems (p = mv) before attempting impulse or collision-based questions.
2. Always define a positive direction before solving collision problems, since momentum is a vector and sign errors are the most common mistake.
3. Practice both elastic and inelastic collision problems separately, since they use different conservation conditions (only inelastic collisions conserve momentum but not kinetic energy).
4. Revisit the impulse-momentum theorem alongside Newton's second law, since exam questions often test the connection between the two rather than either formula in isolation.

Once confident, test recall speed under timed conditions with eSaral's JEE Test Series, which includes a dedicated Laws of Motion mock section.

Which Other eSaral Physics Resources Should Class 11 Students Check Next?

• Class 11 Laws of Motion Notes for JEE & NEET
• NCERT Solutions Class 11 Physics Chapter 4 — Laws of Motion
• What Is Impulse? — Definition, Formula & Solved Examples
• Applications of Impulse — Class 11 Physics
• Linear Momentum Questions and Answers for Class 11 Physics
• Laws of Motion Class 11 Questions with Answers
• Work Energy and Power Class 11 Physics Notes
• CBSE Class 11 Physics Revision Notes with Weightage
• Practice momentum and collision-based JEE Main questions: JEE Main Chapterwise PYQ with Solutions →

Want to master momentum, impulse, and collisions with solved JEE and NEET problems? eSaral's Class 11 Physics course covers Laws of Motion in depth with concept videos by IIT Bombay faculty and chapter-wise practice tests. Explore Class 11 Physics Courses on eSaral →