Physics > Centre of Mass and Conservation of Linear Momentum > 9.0 Newton's law of restitution
Centre of Mass and Conservation of Linear Momentum
1.0 Introduction
2.0 Position of centre of mass of continuous bodies
2.1 Rod
2.2 Semicircular ring
2.3 Semicircular disc
2.4 Solid sphere
2.5 Hemispherical Shell
2.6 Rectangular Plate
2.7 Square Plate
2.8 Circular Plate
2.9 Solid Cone
2.10 Hollow Cone
2.11 Questions
2.12 Centre of mass of a rigid complex bodies
3.0 Centre of mass of the remaining portion
4.0 Laws of conservation of linear momentum
5.0 Variable Mass
6.0 Impulse
7.0 Collision
8.0 Types of collision
9.0 Newton's law of restitution
10.0 Head on elastic and inelastic collision
11.0 Collision in two dimension
12.0 Oblique collision
9.1 For direct collision
2.2 Semicircular ring
2.3 Semicircular disc
2.4 Solid sphere
2.5 Hemispherical Shell
2.6 Rectangular Plate
2.7 Square Plate
2.8 Circular Plate
2.9 Solid Cone
2.10 Hollow Cone
2.11 Questions
2.12 Centre of mass of a rigid complex bodies
$$e = \frac{{{\text{Relative velocity along the common normal just after the impact}}}}{{{\text{Relative velocity along the common normal just before the impact}}}}$$ or $$e = \frac{{{\text{Separation speed}}}}{{{\text{approach speed}}}} = \frac{{{{\overrightarrow v }_2} - {{\overrightarrow v }_1}}}{{{{\overrightarrow u }_1} - {{\overrightarrow u }_2}}}$$
Note: All velocities are along common normal.
The above equation can also be written as, $$e = \frac{{{v_{{2_{CN}}}} - {v_{{1_{CN}}}}}}{{{u_{{1_{CN}}}} - {u_{{2_{CN}}}}}}$$
where, ${{u_{{1_{CN}}}}}$, ${{u_{{2_{CN}}}}}$, ${{v_{{1_{CN}}}}}$ & ${{v_{{2_{CN}}}}}$ are the component of the velocities ${\overrightarrow u _1}$, ${\overrightarrow u _2}$, ${\overrightarrow v _1}$ & ${\overrightarrow v _1}$ along the common normal $(CN)$.