**Branch :**First Year-Engineering Syllabus

**Subject :**Elements of Mechanical Engineering

## Impulse

**Impulse:**** **The product of force and time is defined as linear impulse of the force. Suppose the resultant force (which may be a function of time t) acts from time t_{1} to time t_{2}, then is the total impulse of that duration.

Hence the total linear impulse on a particle of mass *m* equals the corresponding change in the momentum *m v*. In the component forms

If we plot, the resultant force with respect to time, as shown in the following figure, then

Thus, the total impulse between time *t*_{1} and *t*_{2} is the area below the resultant force curve from *t*_{1} to *t*_{2.}

**angular Impulse and Angular Momentum:**The angular momentum M

_{0}of a particle about

*O*is defined as the moment of the linear momentum vector

*m*about O. Thus

**v**

So that,

*H _{x} = m(v_{z}y - v _{y}z)*

*H _{y} = m(v_{x}z - v _{z}x)*

*H _{z} = m(v_{y}x - v _{x}y)* If we take the moment of the forces about O, then

Thus, the moment about the fixed point O of all forces acting on *m* equals the time rate of change of angular momentum of m about O.

Also,

The total angular impulse on *m* about the fixed point O equals the corresponding change in angular momentum of *m* about O.