JEE  >  Additional Documents and Tests for JEE  >  Centrifugal Force

Centrifugal Force Notes | Study Additional Documents and Tests for JEE - JEE

Document Description: Centrifugal Force for JEE 2022 is part of Documents for Additional Documents and Tests for JEE preparation. The notes and questions for Centrifugal Force have been prepared according to the JEE exam syllabus. Information about Centrifugal Force covers topics like Centrifugal Force, Simple Pendulum , Circular Motion in Horizontal Plane , Motion in a Vertical Circle and Centrifugal Force Example, for JEE 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for Centrifugal Force.

Introduction of Centrifugal Force in English is available as part of our Additional Documents and Tests for JEE for JEE & Centrifugal Force in Hindi for Additional Documents and Tests for JEE course. Download more important topics related with Documents, notes, lectures and mock test series for JEE Exam by signing up for free. JEE: Centrifugal Force Notes | Study Additional Documents and Tests for JEE - JEE
Table of contents
Centrifugal Force
Simple Pendulum 
Circular Motion in Horizontal Plane 
Motion in a Vertical Circle
1 Crore+ students have signed up on EduRev. Have you?

Centrifugal Force

When a body is rotating in a circular path and the centripetal force vanishes, the body would leave the circular path. To an observer A who is not sharing the motion along the circular path, the body appears to fly off tangentially at the point of release. To another observer B, who is sharing the motion along the circular path (i.e., the observer B is also rotating with the body which is released, it appears to B, as if it has been thrown off along the radius away from the centre by some force. This inertial force is called centrifugal force.)

Its magnitude is equal to that of the centripetal force = mv2/r . Centrifugal force is a fictitious force which has to be applied as a concept only in a rotating frame of reference to apply Newton's law of motion in that frame)

FBD of ball w.r.t non-inertial frame rotating with the ball.

Centrifugal Force Notes | Study Additional Documents and Tests for JEE - JEE

Suppose we are working from a frame of reference that is rotating at a constant, angular velocity ω with respect to an inertial frame. If we analyse the dynamics of a particle of mass m kept at a distance r from the axis of rotation, we have to assume that a force mrω2 act radially outward on the particle. Only then we can apply Newton's laws of motion in the rotating frame. This radially outward pseudo force is called the centrifugal force.


Simple Pendulum 

A simple pendulum is constructed by attaching a bob of mass m to a string of length L fixed at its upper end. The bob oscillates in a vertical circle. It is found that the speed of the bob is v when the string makes an angle θ with the vertical.

The force acting on the bob are (figure)

Centrifugal Force Notes | Study Additional Documents and Tests for JEE - JEE

(i) Tension T

(ii) Weight mg

As the bob moves in a vertical circle with centre at O, the radial acceleration is v2/L towards O. Taking the components along this radius and applying Newton's second law, we get

Centrifugal Force Notes | Study Additional Documents and Tests for JEE - JEE


Circular Motion in Horizontal Plane 

A ball of mass m attached to a light and inextensible string rotates in a horizontal circle of radius r with an angular speed w about the vertical. If we draw the force diagram of the ball. 

Centrifugal Force Notes | Study Additional Documents and Tests for JEE - JEE

We can easily see that the component of tension force along the centre gives the centripetal force and component of tension along vertical balances the gravitation force. Such a system is called a conical pendulum.


Motion in a Vertical Circle
Suppose a particle of mass m is attached to an inextensible light string of length R. The particle is moving in a vertical circle of radius R about a fixed point O. It is imparted a velocity u in horizontal direction at lowest point A. Let v be its velocity at point B of the circle as shown. 

Centrifugal Force Notes | Study Additional Documents and Tests for JEE - JEE     

h = R(1 - cosθ)   ......(i)         

From conservation of mechanical energy

1/2 m(u2- v2) = mgh

or v= u2 - 2gh   .....(ii)

The necessary centripetal force is provided by the resultant of tension T and mg cosθ

Centrifugal Force Notes | Study Additional Documents and Tests for JEE - JEE......(iii)

Now, following three conditions arise depending on the value of u.

➢ Condition of Looping the Loop (u ≥ √5gR)

The particle will complete the circle if the string does not slack even at the highest point (θ = π). Thus, tension in the string should be greater than or equal to zero (T ≥ 0) at θ = π.  In critical case substituting T = 0 and θ = π in above equation, we get

Centrifugal Force Notes | Study Additional Documents and Tests for JEE - JEE (at highest point)

Substituting θ = π in Eq.(i), h=2R

Therefore, we have

Centrifugal Force Notes | Study Additional Documents and Tests for JEE - JEE

Thus, if u ≥ √5gR , the particle will complete the circle. At u = √5gR, velocity at highest point is v = √gR and tension in the string is zero.

Substituting θ = 0° and  u = √5gR in Eq. (iii), we get T = 6mg or in the critical condition tension in the string at lowest position is 6mg. This is shown in Figure.

Centrifugal Force Notes | Study Additional Documents and Tests for JEE - JEE

If  u < √5gR , following two cases are possible.

➢ Condition of Leaving the Circle (√2gR < u < √5gR)

If u < √5gR the tension in the string will become zero before reaching the highest point. From Eq. (iii), tension in the string becomes zero (T=0)

where,

Centrifugal Force Notes | Study Additional Documents and Tests for JEE - JEE

Substituting this value of cos θ in Eq. (i), we get

Centrifugal Force Notes | Study Additional Documents and Tests for JEE - JEE.......(iv)

or we can say that at height htension in the string becomes zero. Further, if u < √5gR , velocity of the particle becomes zero when

Centrifugal Force Notes | Study Additional Documents and Tests for JEE - JEE.......(v)

i.e. at height h2 velocity of particle becomes zero.

Now, the particle will leave the circle if tension in the string becomes zero but velocity is not zero or T = 0 but v ≠ 0. This is possible only when

Centrifugal Force Notes | Study Additional Documents and Tests for JEE - JEE

Therefore, if √2gR < u < √5gR the particle leaves the circle.

From Eq. (iv), we can see that h R > if u2 > 2gR . Thus, the particle will leave the circle when h >R  or 90 < θ <180 ° . This situation is shown in the Fig.

Centrifugal Force Notes | Study Additional Documents and Tests for JEE - JEE

Note: After leaving the circle, the particle will follow a parabolic path as the particle

comes under gravity.

➢ Condition of Oscillation (0 < u < √2gR)

The particle will oscillate, if velocity of the particle becomes zero but tension in the string is not zero. or v = 0, but T ≠ 0. This is possible when

Centrifugal Force Notes | Study Additional Documents and Tests for JEE - JEE

Moreover, if h1=h2, u = √2gR and tension and velocity both becomes zero simultaneously.

Further, from Eq. (iv), we can see that h ≤ R  if u ≤ √2gR Thus, for 0< u ≤ √2gR 

particle oscillates in lower half of the circle (0°<θ ≤ 90°).

This situation is shown in the figure.

Centrifugal Force Notes | Study Additional Documents and Tests for JEE - JEE

Note: The above three conditions have been derived for a particle moving in a vertical circle attached to a string.The same conditions apply, if a particle moves inside a smooth spherical shell of radius R. The only difference is that the tension is replaced by the normal reaction N.

The document Centrifugal Force Notes | Study Additional Documents and Tests for JEE - JEE is a part of the JEE Course Additional Documents and Tests for JEE.
All you need of JEE at this link: JEE

Related Searches

mock tests for examination

,

Sample Paper

,

Exam

,

pdf

,

Objective type Questions

,

MCQs

,

Previous Year Questions with Solutions

,

Viva Questions

,

Extra Questions

,

practice quizzes

,

video lectures

,

Centrifugal Force Notes | Study Additional Documents and Tests for JEE - JEE

,

Centrifugal Force Notes | Study Additional Documents and Tests for JEE - JEE

,

shortcuts and tricks

,

Centrifugal Force Notes | Study Additional Documents and Tests for JEE - JEE

,

Free

,

Important questions

,

study material

,

past year papers

,

ppt

,

Semester Notes

,

Summary

;