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Curvilinear motion of a particle

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This PPT covers curvilinear motion of an object in a very systematic and lucid manner. I hope this PPT will be helpful for instructor's as well as students.

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Curvilinear motion of a particle

  1. 1. CURVILINEAR MOTION
  2. 2. The motion of an object along a curved path is called a curvilinear motion. Curvilinear motion
  3. 3. Motion of car along a curved road Motion of cable car along a steel cable Curvilinear motion in a plane
  4. 4. Motion of roller coaster along its track. Motion of fighter jets during national parade. Curvilinear motion in a space
  5. 5. Position r 𝑥 𝑖O 𝑥 𝑦 𝑦 𝑗 A r = 𝑥 𝑖 + 𝑦 𝑗 The position of particle at point A in vector form is represented as, The distance of particle from origin is r = 𝑥2 + 𝑦2 Particle′s path
  6. 6. Displacement ri O 𝑥 𝑦 A B rf ∆r The displacement of particle from point A to point B is ∆r = rf − ri ∆r = (𝑥B 𝑖 + 𝑦B 𝑗) − (𝑥A 𝑖 + 𝑦A 𝑗) ∆r = (𝑥B−𝑥A) 𝑖 + (𝑦B−𝑦A) 𝑗 ∆r = ∆𝑥 𝑖 + ∆𝑦 𝑗
  7. 7. Magnitude & direction of displacement ri O 𝑥 𝑦 A B rf ∆r Magnitude: ∆r ∆𝑥 ∆𝑦 θ ∆r = ∆𝑥 2 + ∆𝑦 2 Direction: θ = tan−1 ∆𝑦 ∆𝑥
  8. 8. Average velocity ri O 𝑥 𝑦 A B rf ∆r The average velocity of particle from point A to point B is given by vavg vavg = ∆r ∆t = ∆𝑥 𝑖 + ∆𝑦 𝑗 ∆t vavg = ∆𝑥 ∆t 𝑖 + ∆𝑦 ∆t 𝑗 vavg = vavg−𝑥 𝑖 + vavg−𝑦 𝑗
  9. 9. Magnitude & direction of average velocity ri O 𝑥 𝑦 A B rf ∆r vavg Magnitude: vavg = vavg−𝑥 2 + vavg−𝑦 2 Direction: θ = tan−1 vavg−𝑦 vavg−𝑥 vavg vavg−𝑥 vavg−𝑦 θ
  10. 10. Instantaneous velocity O 𝑥 𝑦 A The instantaneous velocity of particle at point A is given by v v = dr dt = d𝑥 𝑖 + d𝑦 𝑗 dt v = d𝑥 dt 𝑖 + d𝑦 dt 𝑗 v = v 𝑥 𝑖 + v 𝑦 𝑗
  11. 11. v = v 𝑥 2 + v 𝑦 2 Magnitude & direction of instantaneous velocity Magnitude: v v 𝑥 v 𝑦 θ Direction: θ = tan−1 v 𝑦 v 𝑥 O 𝑥 𝑦 A v
  12. 12. Average acceleration vA A B ∆v vB vB -vA vA A B ∆v vB aavg
  13. 13. Average acceleration vA A B vB O 𝑦 𝑥 The average acceleration of particle from point A to point B is given by aavg = ∆v ∆t = ∆v 𝑥 𝑖 + ∆v 𝑦 𝑗 ∆t aavg = ∆v 𝑥 ∆t 𝑖 + ∆v 𝑦 ∆t 𝑗 aavg = aavg−𝑥 𝑖 + aavg−𝑦 𝑗 ∆v aavg
  14. 14. Magnitude & direction of average acceleration vA A B vB O 𝑦 𝑥 aavg aavg−𝑥 aavg−𝑦 Magnitude: aavg = aavg−𝑥 2 + aavg−𝑦 2 Direction: θ = tan−1 aavg−𝑦 aavg−𝑥 θ
  15. 15. Instantaneous acceleration vA A O 𝑦 𝑥 a The instantaneous acceleration of particle at point A is a = dv dt = dv 𝑥 𝑖 + dv 𝑦 𝑗 dt a = dv 𝑥 dt 𝑖 + dv 𝑦 dt 𝑗 a = a 𝑥 𝑖 + a 𝑦 𝑗
  16. 16. Magnitude & direction of instantaneous acceleration vA A O 𝑦 𝑥 a a 𝑥 a 𝑦 θ a = a 𝑥 2 + a 𝑦 2 Magnitude: Direction: θ = tan−1 a 𝑦 a 𝑥
  17. 17. Tangential & normal component of acceleration a at an at = tangential componet of acceleration It changes the speed of particle an = normal componet of acceleration It changes the direction of particle v A
  18. 18. Tangential & normal component of acceleration Speed is constant Speed is increasing Speed is decreasing v a = an v a at an v a at an A A A
  19. 19. Thank you
  • SivaSiva158

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    Jan. 5, 2021
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    Oct. 12, 2020
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    Jul. 18, 2020
  • SagarAjanalkar

    Apr. 30, 2020

This PPT covers curvilinear motion of an object in a very systematic and lucid manner. I hope this PPT will be helpful for instructor's as well as students.

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