System of Particles and Rotational Motion

Notes

Ls 6 Full - Physics - Sugeeth Notes - 11 A - 20-07-23.pdf

Ls 6 - Rotation - Shobhit Nirwan.pdf

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