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Angular Momentum

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Lets take a jump orientation of the motorbike frame changes very little during the course of jump. When it undergoes the jump at each stage you could see the twist or the moment of the body of the driver, this is known as angular momentum. Angular momentum acts where there is twists or turns in the rotational path. Lets see more about this.

What is Angular Momentum?

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The Momentum is nothing but a force associated with the moving body. The angular momentum tells about the momentum in angular path. It is the vector quantity directing itself in direction of angular velocity. It also called moment of momentum or rotational momentum is the measure of the linear momentum for a rotational body having radius r moment with velocity v or measure of moment of inertia I in a rotational path for a body moving with angular velocity $\omega$.

Angular Momentum Equation

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For a body moving in circular path the angular momentum L is
L = pr = mvr
Here m, v and r tells about the mass, velocity and radius of the path.

For a spinning object the angular momentum is
L = I $\omega$Here I tells about the moment of inertia and $\omega$ is the angular velocity
For a rigid body the angular momentum is
L = I $\times$ $\omega$
Here I is the moment of inertia and $\omega$ is the angular velocity
Thus the angular momentum of an object in terms of its components is expressed as
L = $\sum$ Ii $\omega_i$
Here Ii is the moment of inertia of the component, $\omega_i$ is the rotational rate vector of the ith spinning component.
The SI unit of angular momentum is kilogram meter square per second.

Law of Angular Momentum

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Law of conservation of angular momentum states that when no external torque acts on an body or closed system of objects there will no change in angular momentum.It can be stated as:
If the net external torque acting on a system is zero then the change in angular momentum will not be there
$\Delta$ L = 0
or
Li = Lf
Angular momentum before any event = Angular momentum after an event

Angular Momentum and Torque

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Torque is a ability to rotate about an axis due to external force acting whereas the moment or rotation it takes place is what we call angular momentum.The second law of motion tells that the net force acting on the body is equal to the rate of change of its linear momentum.
$\vec{F}$ = $\frac{d(\vec{p})}{dt}$
Multiplying by $\vec{r}$ on both the sides to get
$\vec{r}$ $\times$ $\vec{F}$ = $\vec{r}$ $\times$ $\frac{d \vec{p}}{dt}$
Here $\vec{r}$ $\times$ $\vec{F}$ is the torque that acts on the body.

Angular Momentum Examples

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Here are some day to day examples we see in Angular momentum:
  1. A bullet fired changes its angular momentum at every move.
  2. A Spinning figure skater who spins keeping her arms stretched.Her angular momentum is conserved. Whereas pulling the arms near to the body the moment of inertia decreases increasing the rotational kinetic energy.
  3. Spinning top spins when given a push lightly that changes its angular momentum at the twist.