1 / 9

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.

travis
Télécharger la présentation

Circular Motion

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related