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/83R/8

      • Cone

Locatedβ€…β€Šatβ€…β€Š(3R/4,β€…β€Š1R/4).β€…β€ŠThisβ€…β€Šisβ€…β€Štheβ€…β€Šsupposedβ€…β€Šcentroidβ€…β€Šofβ€…β€Šcone.Located \; at \; (3R/4 , \; 1R/4). \; This \; is \; the \; supposed \; centroid \; of \; cone.
  • Generalised formulas

Radiusmβ€…β€Š=β€…β€Šβˆ‘mxiβˆ‘miRadius_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

      • MassLength\frac{Mass}{Length}= Linear Density

    • Surface Density

      • MassArea\frac{Mass}{Area}= Surface Density

    • Volume Density I.e. Normal Density

      • MassVolume\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

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