---
title: "Work-energy vs impulse-momentum principles"
subject: "Applied Mechanics (Dynamics)"
chapter: 2
key: "semester_3/applied_mechanics_dynamics:work-energy-vs-impulse-momentum"
source: https://www.bctengineer.com/q/semester_3/applied_mechanics_dynamics/work-energy-vs-impulse-momentum
site: BCT Engineering
---

# Work-energy vs impulse-momentum principles

Applied Mechanics (Dynamics) · Chapter 2: Kinetics of particles: Energy and Momentum Methods

- Asked in: 2078 Kartik, 2 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/applied_mechanics_dynamics/work-energy-vs-impulse-momentum
- Whole chapter: https://www.bctengineer.com/md/semester_3/applied_mechanics_dynamics/chapter-2

## Question

Differentiate the concept of "work-energy" and "impulse-momentum" principles for study of kinetics of particle.

## Short answer

Work–energy is a scalar principle relating net work to change in kinetic energy, integrated over displacement. Impulse–momentum is a vector principle relating impulse to change in linear momentum, integrated over time. Work–energy is ideal for problems involving forces acting over distances; impulse–momentum suits impacts and short-duration forces.

## Answer

| Point | Work-energy principle | Impulse-momentum principle |
|---|---|---|
| Statement | Work done by all forces = change in kinetic energy | Impulse of all forces = change in linear momentum |
| Equation | $T_1+U_{1\to2}=T_2$ | $m\vec v_1+\int\vec F\,dt=m\vec v_2$ |
| Quantity | Scalar | Vector (components needed) |
| Force integrated over | Displacement (position) | Time |
| Best used when | Forces and distances are known (springs, gravity, friction over a path) | Forces and times are known, or in impact and short-duration forces |
| Unknowns found | Speed (direction is not given) | Velocity with direction; also impulsive forces |
| Internal/normal forces | Normal force that does no work is ignored | All forces including normal reactions must be included |

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Which is correct about the nature of the two principles?
   A. Work-energy is a scalar relation; impulse-momentum is a vector relation
   B. Both are scalar relations
   C. Work-energy is a vector relation; impulse-momentum is scalar
   D. Both are vector relations
   Answer: A. Energy is scalar, so no components are needed; momentum is a vector and needs components. (Key point: Quantity type)

2. What does the work-energy principle integrate force over, compared with impulse-momentum?
   A. Time, whereas impulse-momentum uses displacement
   B. Velocity, whereas impulse-momentum uses time
   C. Displacement, whereas impulse-momentum uses time
   D. Displacement in both
   Answer: C. Work = integral of F ds (position); impulse = integral of F dt (time). (Key point: Force integrated over)

3. For a short-duration impact where force and time are known, which principle is best?
   A. Work-energy
   B. Impulse-momentum
   C. Conservation of mass
   D. Either gives direction without components
   Answer: B. Impulse-momentum suits impact and short-duration forces, and also gives velocity direction. (Key point: Choice of method)

4. How are smooth-surface normal forces treated?
   A. Ignored in both principles
   B. Included in both principles
   C. Ignored in work-energy (no work) but included in impulse-momentum
   D. Included in work-energy but ignored in impulse-momentum
   Answer: C. A normal force that does no work drops out of work-energy, but impulse-momentum must include all forces. (Key point: Normal forces)

## Related in Applied Mechanics (Dynamics)

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