Motion in Two and Three Dimensions

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Physics Newtonian Mechanics Motion in Two and Three Dimensions

	Uniform Circular Motion:
	The circular motion of an object takes place in a two dimensional plane. The plane can be horizontal or vertical. When an object moves in a circular path of radius ‘r’ with a uniform speed, then the motion of the object is called uniform circular motion. The acceleration of this nature is called centripetal acceleration given by, a_r = v²/r, where v is the speed of the object. Derivation is given below Consider the triangles in the figure. Then the similarity principle implies: Δv/v = Δr/r Using this expression in the above relation we get Since, Δr/Δt --> v as Δt --> 0. Thus, the radial acceleration can be expressed as: The total acceleration of the object undergoing circular motion will be the sum of its radial acceleration and the translational acceleration. The translational acceleration is the rate of change of its translational velocity. Since these two vectors are perpendicular to each other, the resultant acceleration will be: The force which acts towards the centre of the circular path is called centripetal force and is obtained as the product of mass time the centripetal acceleration.