Angular Momentum Of A Rod

Momentum is the product of mass and the velocity of the object. Any object moving with mass possesses momentum. The only difference in angular momentum is that it deals with rotating or spinning objects. So is it the rotational equivalent of linear momentum?

What is Angular Momentum?

If yous try to become on a wheel and balance without a kickstand, you volition probably fall off. Simply one time you lot start pedalling, these wheels selection up angular momentum. They are going to resist change, thereby making balancing gets easier.

Angular momentum is divers as:

The property of whatever rotating object given by moment of inertia times angular velocity.

It is the property of a rotating body given by the product of the moment of inertia and the angular velocity of the rotating object. It is a vector quantity, which implies that the management is also considered here along with magnitude.

Symbol	The athwart momentum is a vector quantity, denoted by \(\begin{array}{50}\vec{50}\stop{assortment} \)
Units	Information technology is measured using SI base of operations units: Kg.mⁱⁱ.s^-i
Dimensional formula	The dimensional formula is: [M][L]²[T]^-ane

You may also desire to check out these topics given below!

Relation Between Torque And Moment Of Inertia
Relation Between Torque And Speed
Radial Acceleration
Relation Between Kinetic Energy And Momentum

Athwart Momentum Formula

Angular momentum can be experienced past an object in ii situations. They are:

Signal object:The object accelerating around a fixed point. For example, World revolving effectually the lord's day. Here the athwart momentum is given by:

\(\brainstorm{array}{l}\vec{Fifty}=\vec{r}\times \vec{p}\end{assortment} \)

Where,

\(\begin{assortment}{fifty}\vec{L}\,is\,the\,angular\,velocity\cease{array} \)
r is the radius (distance between the object and the stock-still point about which it revolves)
\(\begin{array}{l}\vec{p}\,is\,the\,linear\,momentum.\end{array} \)

Extended object: The object, which is rotating about a fixed bespeak. For example, Earth rotates about its centrality. Here the athwart momentum is given by:

\(\brainstorm{array}{l}\vec{L}=\vec{I}\times \vec{\omega }\end{array} \)

Where,

\(\begin{array}{l}\vec{L}\,is\,the\,athwart\,momentum.\end{array} \)
I is the rotational inertia.
\(\brainstorm{array}{l} \vec{\omega }\,is\,the\,angular\,velocity.\stop{assortment} \)

Angular Momentum Formula

Athwart Momentum Quantum Number

Angular momentum quantum number is synonymous with Azimuthal quantum number or secondary breakthrough number. Information technology is a breakthrough number of an atomic orbital that decides the athwart momentum and describes the size and shape of the orbital. The typical value ranges from 0 to one.

Right-Mitt Rule

Right-Hand Rule

The management of athwart momentum is given by the right-paw rule, which states that:

If you position your correct hand such that the fingers are in the direction of r.
Then roll them around your palm such that they point towards the management of Linear momentum(p).
The outstretched pollex gives the direction of angular momentum(Fifty).

The video explains a problem based on the conservation of angular momentum. The solution to this physics merry-go-circular problem is explained with the aid of animations for your improve understanding.

Examples of Angular Momentum

We knowingly or unknowingly come up across this holding in many instances. Some examples are explained below.

Ice-skater

When an ice-skater goes for a spin she starts off with her hands and legs far autonomously from the eye of her body. Just when she needs more angular velocity to spin, she gets her hands and leg closer to her trunk. Hence, her athwart momentum is conserved, and she spins faster.

Gyroscope

A gyroscope uses the principle of athwart momentum to maintain its orientation. It utilises a spinning wheel that has 3 degrees of freedom. When it is rotated at high speed it locks on to the orientation, and it won't deviate from its orientation. This is useful in space applications where the attitude of a spacecraft is a really of import factor to exist controlled.

Frequently Asked Questions – FAQs

Calculate the angular momentum of a pulley of ii kg, radius 0.1 thou, rotating at a constant angular velocity of 4 rad/sec

Substitute the given values similar m=2 kg and r=0.ane yard in I=(1/2)mr² (formula of the moment of inertia) we get I= 0.01 kg.m²
Angular momentum is given by L=Iω, thus, substituting the values we get L=0.04 kg.g².s-¹.

Give the expression for Angular momentum.

\(\begin{array}{50}\vec{Fifty}=\vec{I} \times \vec{\omega }\cease{array} \)

\(\begin{array}{l}\vec{L}=\vec{r} \times \vec{p}\end{array} \)

For an isolated rotating torso, how are angular velocity and radius related?

For an isolated rotating body, athwart velocity is inversely proportional to the radius.

Write the dimensional formula for Athwart momentum.

The dimensional formula is ML^twoT^-1

When an water ice-skater goes for a spin, what happens to her spinning speed when she stretches her hands?

How can an ice-skater increase his/her spinning speed?

By bringing easily closer, thus reducing the radius increases the angular velocity.

If the moment of inertia of an isolated system is halved. What happens to its angular velocity?

Athwart velocity volition be doubled.

Calculate the angular moment of the object. When an object with the moment of inertia I = v kg.m² is made to rotate ane rad/sec speed.

Substituting the given value in formula L=Iω we get L=five kg.m².south^-1.

Stay tuned with BYJU'S for more than such interesting articles. Likewise, download BYJU'Southward – The Learning App for loads of interactive, engaging Physics videos with unlimited academic aid.