Physics - Centripetal Acceleration and Centripetal Force

1. Centripetal Acceleration
- Debopam Bhattacharya

2. Driving a car or a cycle on a straight road is easy, but have ever thought why your
dad shouts when you make a sharp turn on a circular path ?
Why do you have to handle the steering wheel with a extra grip as you navigate a
curve ?
OR
Have you ever pondered why you were able to enjoy the merry-go-round as a child
?
Well, the answer is Centripetal Force and Centripetal Acceleration

3. ▪ Centripetal Force
▪ Centripetal Acceleration
WHAT WE WILL LEARN INTHIS SLIDE ?

4. CENTRIPETAL FORCE
Suppose you and your friends are riding a cycle to the nearest
football ground.
On your path you experience a big circular curve, bravely you and
your friends continue on your path.
You all continue to pedal at a uniform speed and maintain a constant
speed. As you move along the circular path, the direction
continuously changes.
You wonder how you were able to easily cover the path ?
Well, the answer is hidden the physics of your motion
It is known as CENTRIPETAL FORCE

5. CENTRIPETAL FORCE
CENTRIPETAL FORCE – is that force which is required to move an object
in a circular path with constant speed and it acts on the object along the
radius of the circular path and towards the centre of the circular path.
F
F F
F
v
v
v
v

6. Q. Can an object moving with constant speed have an acceleration ??
Yes, absolutely if it is changing it’s direction.
Q. Does a body in uniform circular motion has acceleration ?
Yes, and it is known as CENTRIPETAL ACCELERATION.
CENTRIPETAL ACCELERATION – is the acceleration produced in the
motion of object by centripetal force when they are moving in a circular
path.

7. CENTRIPETAL ACCELERATION
Suppose superman whose mass is ‘m’ is moving on a
circular path of radius r with constant speed v. It
travels B to C in time Δt.
‘Velocity’ (not speed, it is velocity) changes from 𝑣1to
𝑣2
Thus the change in velocity :
∆𝑣 = 𝑣2 − 𝑣1
∆𝑣 = 𝑣2
2
+ 𝑣1
2
− 2𝑣1 𝑣2 𝑐𝑜𝑠𝜃
∆𝑣 = 𝑣2 + 𝑣2 − 2𝑣2 𝑐𝑜𝑠𝜃

8. ∆𝑣 = 2𝑣2[1 − 𝑐𝑜𝑠𝜃]
∆𝑣 = 2𝑣𝑠𝑖𝑛(
𝜃
2
)
If s is the distance travelled from B to C
𝑠 = 𝑟𝜃
∆𝑡 =
𝑠
𝑣
=
𝑟𝜃
𝑣
Thus the centripetal acceleration is given by,
𝑎 𝑐 =
∆𝑣
∆𝑡
𝑎 𝑐 =
2𝑣𝑠𝑖𝑛
𝜃
2
𝑟𝜃
𝑣
sin^2(x) = 1/2 - 1/2 cos(2x){ }

9. 𝑎 𝑐 =
𝑣2 sin
𝜃
2
𝑟
𝜃
2
If θ is very small , then
sin
𝜃
2
=
𝜃
2
CENTRIPETAL ACCELERATION IS
𝑎 𝑐 =
𝑣2
𝑟
CENTRIPETAL FORCE IS
𝐹𝑐 =
𝑚𝑣2
𝑟

10. Q. What is the magnitude of the centripetal acceleration
of a car following a curve, see figure below, of radius
500 m at a speed of 25 m/s—about 90 km/hr? Compare
the acceleration with that due to gravity for this fairly
gentle curve taken at highway speed.

11. THANKYOU
Debopam Bhattacharya
debopamhappy@gmail.com