Circular Motion β Solved Examples
Example 1: Find the angular velocity of the boy who is riding the bicycle at a speed of 10 ms-1 on a circular path of radius 25 m.
Solution:
We have given,
- Linear speed of the boy as he is riding the bicycle, V = 10 ms-1
- Radius of the circular path, R = 25 m
We know that, the angular velocity of the boy riding the bicycle on a circular path can be obtained by using the given formula,
Substituting the value of V and R in the formula of angular velocity, we get,
Therefore, the angular velocity (Ο) of the boy who is riding the bicycle at a speed of 10 ms-1 on a circular path of radius 25 m is 0.4 rad s-1 .
Example 2: In the above problem, if the mass of the boy is 35 kg then calculate the centripetal acceleration of the boy and also find the centrifugal force acting on the boy.
Solution:
We know that centripetal acceleration is given by,
Substituting the value of V and R in above formula, we get,
ac = 4 ms-2
Now, the centrifugal force can be given by the,
As the mass of the boy is given to be m = 35 kg, therefore,
Fc = 140 N
Therefore, centripetal acceleration of the boy is 4 ms-2 and the centrifugal force experienced by the boy is 140 N.
Example 3: Suppose a motorcyclist is making a turn at a speed of 10 ms-2. How will the force acting towards the centre will change if he doubles its speed?
Solution:
As we know, the centripetal force is given by,
Since, the centripetal force is directly proportional to the square of the speed, i.e.,
Therefore, when the speed will get doubles, the centripetal force acting on the motorcyclist will increase to 4 times.
Example 4: A car is going in a non-uniform motion on curve of circular path, and its tangential acceleration is given as 3 ms-2, while its centripetal acceleration is given as 4 ms-2. Calculate its total acceleration.
Solution:
Given,
- Tangential Acceleration (at) = 3 ms-2
- Centripetal Acceleration (ac) = 4 ms-2
We know that the total acceleration is given by,
Substituting values, we get,
Therefore the total acceleration is 5 ms-2.
Example 5: An insect is trapped in a circular groove of radius 10 cm moves along the groove steadily and completes 5 revolutions in 100 seconds. What is the angular speed and linear speed of the motion?
Solution:
Given,
- Radius, R = 10 cm
- Total revolution made =
- Time taken, T = 100 s
Therefore angular speed, Ο is given by,
The linear speed, V is given by,
V = ΟR
Therefore, the angular speed is and the linear speed is .
Circular Motion
Circular Motion is defined as the movement of an object rotating along a circular path. Objects in a circular motion can be performing either uniform or non-uniform circular motion. Motion of a car on a bank road, the motion of a bike well of death, etc. are examples of circular motion.
In this article, we will learn about circular motion and some related concepts, such as examples, equations, applications, etc.
Table of Content
- What is Circular Motion?
- Equations for Circular Motion
- Centripetal Force
- Centrifugal Force
- Types of Circular Motion
- Circular Motion and Rotational Motion
- Circular Motion Formulas