# System of Particles and Rotational Motion

## Notes

[Ls 6 Full - Physics - Sugeeth Notes - 11 A - 20-07-23.pdf](https://drive.google.com/file/d/1M45bBWd_zhDVSIajMqq-j7iO5mf9dd-N/view?usp=drivesdk)

[Ls 6 - Rotation - Shobhit Nirwan.pdf](https://drive.google.com/file/d/1OgOb53GO_wuakkiYN3O_GKvxk8j0lMRV/view?usp=drive_link)

## Key Concepts

* Centre of Mass
  * Regular Objects:-
    * Square
    * Rectangle
    * Circle
    * Cylinder
    * Sphere
    * Cube / Cuboid
    * Hemisphere from the base = $$3R/8$$
    * Cone

$$
Located ; at ; (3R/4 , ; 1R/4). ; This ; is ; the ; supposed ; centroid ; of ; cone.
$$

* Generalised formulas

$$
Radius\_m ; = ; \frac{\sum mx\_i}{\sum m\_i}
$$

```
     There are multiple variations of this formula, including the integrated version.
```

* Determining the distance of objects from the COM given.
* Concepts of Density
  * Linear Density
    * $$\frac{Mass}{Length}$$= Linear Density
  * Surface Density
    * $$\frac{Mass}{Area}$$= Surface Density
  * Volume Density I.e. Normal Density
    * $$\frac{Mass}{Volume}$$= Density
* Moment of Inertia
  * Disc, Ring, Sphere, Shell, and Complex figures.
* Rotational Motion
  * Intro to Rotational Quantities
  * Intro to Angular Momentum
  * Determining relationship between Inertia and Angular Velocity through virtue of Conservation of Angular Momentum
  * Intro to Torque, Radius of Gyration
  * Rotational Motion and Rolling Motion
  * Ratio between Total K.E and Rotational K.E.
* Miscellaneous Concepts