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2c_lec5 - Physics 2A Olga Dudko UCSD Physics Lecture 5...

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Today: Circular motion. Newton’s Laws of Motion. Laws that answer “why” questions about motion. Forces. Inertia. Momentum. Physics 2A Olga Dudko UCSD Physics Lecture 5
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Uniform Circular Motion • An important case of accelerated motion in 2D is uniform circular motion - the motion of an object describing a circular path at constant speed . • Although the speed is constant, the motion is accelerated because… • The velocity vectors are tangent to the circle at every instant of motion. v the direction of the velocity is changing.
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• In uniform circular motion, the acceleration vector is always perpendicular to the velocity: Perpendicular velocity and acceleration a When acceleration is always perpendicular to velocity, then only the direction of velocity changes and not the magnitude. v ( t ) a v ( t + Δ t )
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• This acceleration is known as radial acceleration, a r , or centripetal acceleration, a c . • “Centripetal” = “center-seeking.” • The magnitude of centripetal acceleration is given by while the direction of centripetal acceleration always points toward the center of the circular motion. Centripetal Acceleration a r = v 2 r a v ( t ) a v ( t + Δ t )
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• An object moving in a curved path with varying speed is in nonuniform circular motion. Nonuniform circular motion a v a r a t a r = v 2 / r a a r a t a = a r 2 + a t 2 • Both direction and magnitude of the velocity are changing => acceleration cannot be strictly || or to the velocity. a a r a t = + tangential acceleration radial acceleration a t = dv / dt a r changes only the direction of the velocity a t changes only the magnitude of the velocity.
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