Some Terminology

• The distance from te axis at which if its entire mass (M) be supposed to be concentrated at...}
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Theorems in Rotational Dynamics

• Theorem of parallel axis state that  The moment of inertia of a rigid body about...}
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Moment of Inertia of a Rectangular Lamina

parallel axis theorem, perpendicular axis theorem.

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Moment of Inertia of a Ring

MI of ring about an axis perpendicular to the plane and passing through CG:\begin{align*}I=MR^{2}...}

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Moment of Inertia of a Circular Disc

MI of circular disc about an axis perpendicular to the plane and passing through CG:\begin{align*...}

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Moment of Inertia of an Annular disc

MI of the annular disc.

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Moment of Inertia of Solid sphere

• moment of inertia of solid sphere about a diameter:\begin{align*}I=\frac{2MR^{2}}{5}\end{al...}
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Moment of Inertia of a Spherical shell (hollow sphere)

• Moment of inertia of a spherical shell about diameter is  $$I=\frac{2MR^2}{3}$$
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Moment of Inertia of a Solid Cylinder

• MI of solid cylinder about the axis through its centre and perpendicular to its plane:
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Moment of Inertia of a Hollow cylinder

Moment of inertia of the hollow cylinder about the axis passing through its center and perpendicu...}

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Kinetic Energy of a Rigid body

• units of K.E. is ergs in cgs system joules in MKS SYSTEM and foot pounds in FPS system
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Acceleration of an Object Rolling Down an Inclined Plane

mathematical form of acceration of rolling body on inclined plane.

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Equation of Motion of a Rotating Rigid body

mathematical form of torque and angular momentum.

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