Physics > Rotational Dynamics > 3.0 Relation between torque and angular momentum
Rotational Dynamics
1.0 Introduction
1.1 Torque or moment of a force
1.2 Relation between torque and moment of inertia
1.3 Pseudo torque
1.4 Torque equation
1.5 Principal of moments
2.0 Angular momentum or moment of a momentum
3.0 Relation between torque and angular momentum
4.0 Combined translational and rotational motion of a rigid body
5.0 Rotational kinetic energy
6.0 Uniform pure rolling
7.0 Accelerated pure rolling
8.0 Instantaneous axis of rotation
9.0 Toppling
3.1 Conservation of angular momentum
1.2 Relation between torque and moment of inertia
1.3 Pseudo torque
1.4 Torque equation
1.5 Principal of moments
Angular impulse of a torque in a given time is equal to the change in angular momentum during that time.
Angular impulse is denoted by a symbol $\overrightarrow J $.
If angular momentum of a body is changed by a torque $\left( {\overrightarrow \tau } \right)$ between time $t_1$ and $t_2$, then $$\overrightarrow J = \int\limits_{{t_1}}^{{t_2}} {\overrightarrow \tau dt} $$ or $$\begin{equation} \begin{aligned} \overrightarrow J = \int\limits_{{t_1}}^{{t_2}} {\frac{{d\overrightarrow L }}{{dt}}dt} \\ \overrightarrow J = \int\limits_{{L_1}}^{{L_2}} {d\overrightarrow L } \\ \overrightarrow J = {\overrightarrow L _2} - {\overrightarrow L _1} \\ \overrightarrow J = \Delta \overrightarrow L \\\end{aligned} \end{equation} $$
Angular impulse is also defined as the moment of linear impulse.
Mathematically, $$\overrightarrow J = \overrightarrow r \times \overrightarrow I $$
where,
$\overrightarrow I $: is the linear impulse
$\overrightarrow r $: is the radius vector about a given point
