Solved Examples on Centripetal Acceleration
Example 1: Find the centripetal acceleration on an object performing circular motion with a radius of 5m. The velocity of the object is 10m/s.
Solution:
The centripetal acceleration is given by,
a = v2/r
Given:
v = 10m/s.
r = 5m.
Plugging the values in the equation,
a = v2/r
⇒ a = (10)2/(5)
⇒ a = 100/5
⇒ a = 20 m/s2
Example 2: Find the centripetal acceleration on an object performing circular motion with a radius of 20m. The velocity of the object is 100m/s.
Solution:
The centripetal acceleration is given by,
a = v2/r
Given:
v = 100m/s.
r = 20m.
Plugging the values in the equation,
a = v2/r
⇒ a = (100)2/(20)
⇒ a = 10000/20
⇒ a = 500 m/s2
Example 3: An object(m = 5Kg) is performing circular motion with radius 2m. If the velocity of the object is 8 m/s, find the centripetal force acting on the object.
Solution:
The centripetal acceleration is given by,
a = v2/r
Given:
v = 8m/s.
r = 2m.
Plugging the values in the equation,
a = v2/r
⇒ a = (8)2/(2)
⇒ a = 64/2
⇒ a = 32 m/s2
Force acting on the object is given by,
F = ma
⇒ F = (5)(32)
⇒ F = 160 N
Example 4: An object(m = 2Kg) is performing circular motion with radius 5m. If the velocity of the object is 10 m/s, find the centripetal force acting on the object.
Solution:
The centripetal acceleration is given by,
a = v2/r
Given:
v = 10m/s.
r = 5m.
Plugging the values in the equation,
a = v2/r
⇒ a = (10)2/(5)
⇒ a = 100/5
⇒ a = 20 m/s2
Force acting on the object is given by,
F = ma
⇒ F = (2)(20)
⇒ F = 40 N
Example 5: An object(m = 2Kg) is performing circular motion with radius 5m. If the centripetal force acting on the object is 100N, find the velocity of the object.
Solution:
Force acting on the object is given by,
F = ma
⇒ 100 = (2)(a)
⇒ a = 50 m/s2
The acceleration of the object is given by,
a = v2/r
⇒ 50 = v2/5
⇒ 250 = v2
⇒ v = 5√10 m/s.
Centripetal Acceleration
Centripetal acceleration refers to the acceleration experienced by an object moving in a circular route. Unlike linear acceleration, which changes an item’s speed in a straight line, centripetal acceleration alters the direction of motion, causing the object to constantly shift its velocity vector in order to maintain circular motion.
There are a lot of objects around us in real life that are constantly performing circular motion, even our planet revolves around the sun in a similar fashion. It is known that velocity is a vector quantity and any object performing circular motion is undergoing a change of velocity. Since there is a change in velocity, a force must be there that acts on the body to change its velocity continuously and make it perform the circular motion. This change in velocity is called acceleration. In this article, we will learn in detail about centripetal acceleration, its formula, derivation, and applications.
Table of Content
- What is Centripetal Acceleration?
- Centripetal Acceleration Formula
- Characteristics of Centripetal Acceleration
- Centripetal Force
- Application of Centripetal Acceleration