Rotational dynamics

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Physics Newtonian Mechanics Rotational dynamics

	Rotational Inertia of Solid Bodies:
	A solid body can be described by a continuous mass density function ρ(r). Then the rotational inertial / moment of inertia of the solid body about a known axis can be calculated by integrating the square of the distance (weighted by the mass density) from a point in the body to the rotation axis: where V is the volume occupied by the object, ρ is the spatial density function of the object, and r represents the coordinates of a point inside the body: Based on dimensional analysis alone, the moment of inertia of a non-point object with mass M, and radius R from the center of mass must take the form: where k is a dimensionless constant called the inertia constant that varies with the object in consideration. Torque due to gravity: When an object is undergoing rotational motion in the field of gravity then the acceleration of the object is equal to the acceleration due to gravity. And the force acting on the object is given by, F= mg where α = g/r is the rotational acceleration Or ∑r × F = m α(r•r) – r(r•α) = m α r2 – 0 = mr2 α ∑r × F = Iα ∑τ = Ig/r This expression gives the total torque acting on the object undergoing rotational motion in the field of gravity.