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Circular Motion

Circular Motion. Deriving the formula for centripetal acceleration. Deriving Formula for Centripetal Acceleration. v. r is the radius of the circle that the object is traveling v is the tangential velocity r and v form a right triangle. r. Deriving Formula for Centripetal Acceleration.

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Circular Motion

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  1. Circular Motion Deriving the formula for centripetal acceleration

  2. Deriving Formula for Centripetal Acceleration v r is the radius of the circle that the object is traveling v is the tangential velocity r and v form a right triangle r

  3. Deriving Formula for Centripetal Acceleration v1 Θ v2 r r Angle between r of 1st triangle and 2nd triangle = θ Angle between hypoteneuse of 1st triangle and hypotenuse of 2nd triangle = θ Thus, angle between v of 1st triangle and 2nd triangle = θ Θ

  4. Deriving Formula for Centripetal Acceleration v1 l One triangle is formed using the two points where we determined the velocity The angle across from l is θ v2 r r

  5. Deriving Formula for Centripetal Acceleration v1 v1 Δv v2 l v2 r r Another triangle is formed with the velocity vectors Note – the vectors are being subtracted because they are tail to tail Δv = v2 – v1 The angle across from Δv is θ

  6. Deriving Formula for Centripetal Acceleration v1 v1 Δv v2 l v2 r r If the object is being swung with a constant speed then the magnitude of v1 and the magnitude of v2 are equal. Thus – the two triangles are similar v1 = Δv rl

  7. Deriving Formula for Centripetal Acceleration v1 = Δv r l Δv = v1l r Divide both sides by Δt Δv = v1l ΔtΔt r

  8. Deriving Formula for Centripetal Acceleration Δv = v1l ΔtΔt r Δv = a Δt v = l Δt So . . . . . .

  9. Deriving Formula for Centripetal Acceleration a = v2 r

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