Rotational Dynamics

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Circular motion is the motion of an object along a circular path. Revolution: The object (or every particle in the object) undergoes circular motion about some point outside the object or about anothe

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v = ωr (magnitude) v⃗ = ω⃗ × r⃗ (vector form) Where: v = tangential velocity, ω = angular velocity, r = radius Direction of ω is given by right-hand thumb rule along the axis of rotation.

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Centripetal acceleration is the acceleration directed towards the center of circular motion, responsible for changing the direction of velocity. Derivation: For UCM, speed is constant but direction c

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Centripetal Force (CPF): Real force directed towards center, required for circular motion. CPF = mω²r = mv²/r Centrifugal Force (CFF): Pseudo force directed away from center, experienced in rotating

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Given: r = 50 m, vmax = 20 m/s, g = 10 m/s² Find: μs (coefficient of static friction) Formula: For horizontal circular motion, friction provides centripetal force fs,max = μsN = μsmg = mv²max/r Solu

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In well of death, vehicle moves in horizontal circles on vertical cylindrical wall. Forces: N (horizontal, towards center), mg (downward), fs (upward) For circular motion: N = mv²/r For vertical equ

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Banking: Tilting of curved road surfaces at angle θ with horizontal to reduce dependence on friction. Forces on banked road: mg (downward), N (perpendicular to road surface) For equilibrium: Vertica

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Conical Pendulum: A pendulum whose bob moves in horizontal circle while string traces a cone. Forces: mg (downward), T (along string) At angle θ with vertical: Vertical equilibrium: T cos θ = mg Hor