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Uniform Circular Motion

Uniform Circular Motion. Deriving a R = v 2 /r Where a R is radial acceleration (Due to change in direction.). Uniform Circular Motion. Means that an object is moving in a circle at a c onstant speed. Thus the magnitude remains constant but the direction is always changing.

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Uniform Circular Motion

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  1. Uniform Circular Motion Deriving aR = v2/r Where aRis radial acceleration (Due to change in direction.)

  2. Uniform Circular Motion • Means that an object is moving in a circle at a constant speed. Thus the magnitude remains constant but the direction is always changing.

  3. Deriving formula for acceleration:

  4. Δr r r

  5. Getting to aR = v2/r Δr is the displacement along the arc. Letting Δt be very small, Δθ between two velocity vectors and corresponding radius positions is the same, thus Δv/v is geometrically equal to Δr/r. Δv = (v/r) Δr, then take this equation and divide both sides by Δt since we are looking for a. By definition a = Δv/Δt, We get aR = (v Δr)/(r Δt) Since Δr/Δt = v, aR = v2/r

  6. Remarks: • Velocity is always tangent to the circle. • Circular motion is always clockwise. • The direction of acceleration is always pointing in to the center of the circle and that is considered the positive direction. The reason it points toward the center is because Δv points that way and it is in the same direction. Also.

  7. Additional Formulas • V = velocity • V = 2πr/T = circumference/period = distance/time • T = period = time for one rotation or cycle • f = frequency = 1/T, measured in Hertz

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