World Library  
Flag as Inappropriate
Email this Article

Impulse (physics)

Article Id: WHEBN0000211922
Reproduction Date:

Title: Impulse (physics)  
Author: World Heritage Encyclopedia
Language: English
Subject: Classical mechanics, Momentum, Force, Pelton wheel, Gravity tractor
Publisher: World Heritage Encyclopedia

Impulse (physics)

Common symbols J, Imp
SI unit N · s = kg · m/s

In classical mechanics, impulse (symbolized by J or Imp[1]) is the product of a force, F, and the time, t, for which it acts. The impulse of a force acting for a given time interval is equal to the change in linear momentum produced over that interval.[2] Impulse is a vector quantity since it is the result of integrating force, a vector quantity, over time. The SI unit of impulse is the newton second (N·s) or, in base units, the kilogram meter per second (kg·m/s).

A resultant force causes acceleration and a change in the velocity of the body for as long as it acts. A resultant force applied over a longer time therefore produces a bigger change in linear momentum than the same force applied briefly: the change in momentum is equal to the product of the average force and duration. Conversely, a small force applied for a long time produces the same change in momentum—the same impulse—as a larger force applied briefly.

J = F_{average} (t_2 - t_1)

The impulse is the integral of the resultant force (F) with respect to time:

J = \int F dt

Mathematical derivation in the case of an object of constant mass

The impulse delivered by the sad[3] ball is mv0, where v0 is the speed upon impact. To the extent that it bounces back with speed v0, the happy ball delivers an impulse of mΔv=2mv0.

Impulse J produced from time t1 to t2 is defined to be[4]

\mathbf{J} = \int_{t_1}^{t_2} \mathbf{F}\, dt

where F is the resultant force applied from t1 to t2.

From Newton's second law, force is related to momentum p by

\mathbf{F} = \frac{d\mathbf{p}}{dt}


\begin{align} \mathbf{J} &= \int_{t_1}^{t_2} \frac{d\mathbf{p}}{dt}\, dt \\ &= \int_{p_1}^{p_2} d\mathbf{p} \\ &= \mathbf{p_2} - \mathbf{p_1} = \Delta \mathbf{p} \end{align}

where Δp is the change in linear momentum from time t1 to t2. This is often called the impulse-momentum theorem.[5]

As a result, an impulse may also be regarded as the change in momentum of an object to which a resultant force is applied. The impulse may be expressed in a simpler form when the mass is constant:

\mathbf{J} = \int_{t_1}^{t_2} \mathbf{F}\, dt = \Delta\mathbf{p} = m \mathbf{v_2} - m \mathbf{v_1}


F is the resultant force applied,
t1 and t2 are times when the impulse begins and ends, respectively,
m is the mass of the object,
v2 is the final velocity of the object at the end of the time interval, and
v1 is the initial velocity of the object when the time interval begins.

The term "impulse" is also used to refer to a fast-acting force or impact. This type of impulse is often idealized so that the change in momentum produced by the force happens with no change in time. This sort of change is a step change, and is not physically possible. However, this is a useful model for computing the effects of ideal collisions (such as in game physics engines).

A large force applied for a very short duration, such as a golf shot, is often described as the club giving the ball an impulse.

Impulse has the same units (in the International System of Units, kg·m/s = N·s) and dimensions (MLT−1) as momentum.

Variable mass

The application of Newton's second law for variable mass leads to the Tsiolkovsky rocket equation.

See also


  1. ^ Beer, F.P., E.R. Johnston, Jr., D.F. Mazurek, P.J. Cornwell, and E.R. Eisenberg. (2010). Vector Mechanics for Engineers; Statics and Dynamics. 9th ed. Toronto: McGraw-Hill.
  2. ^ Impulse of Force, Hyperphysics
  3. ^
  4. ^ Hibbeler, Russell C. (2010). Engineering Mechanics (12th ed.). Pearson Prentice Hall. p. 222.  
  5. ^ See, for example, section 9.2, page 257, of Serway (2004).


External links

  • Dynamics
This article was sourced from Creative Commons Attribution-ShareAlike License; additional terms may apply. World Heritage Encyclopedia content is assembled from numerous content providers, Open Access Publishing, and in compliance with The Fair Access to Science and Technology Research Act (FASTR), Wikimedia Foundation, Inc., Public Library of Science, The Encyclopedia of Life, Open Book Publishers (OBP), PubMed, U.S. National Library of Medicine, National Center for Biotechnology Information, U.S. National Library of Medicine, National Institutes of Health (NIH), U.S. Department of Health & Human Services, and, which sources content from all federal, state, local, tribal, and territorial government publication portals (.gov, .mil, .edu). Funding for and content contributors is made possible from the U.S. Congress, E-Government Act of 2002.
Crowd sourced content that is contributed to World Heritage Encyclopedia is peer reviewed and edited by our editorial staff to ensure quality scholarly research articles.
By using this site, you agree to the Terms of Use and Privacy Policy. World Heritage Encyclopedia™ is a registered trademark of the World Public Library Association, a non-profit organization.

Copyright © World Library Foundation. All rights reserved. eBooks from World eBook Library are sponsored by the World Library Foundation,
a 501c(4) Member's Support Non-Profit Organization, and is NOT affiliated with any governmental agency or department.