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.

1. CURVILINEAR
MOTION

2. The motion of an object along
a curved path is called
a curvilinear motion.
Curvilinear motion

3. Motion of car along a
curved road
Motion of cable car along a
steel cable
Curvilinear motion in a plane

4. Motion of roller coaster along
its track.
Motion of fighter jets during
national parade.
Curvilinear motion in a space

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. 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. 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. 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. 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. 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. 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. Average acceleration
vA
A
B
∆v
vB
vB
-vA
vA
A
B
∆v
vB
aavg

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. 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. 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. 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. 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. 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. Thank
you