Circular Motion Notes With JEE NEET MCQS Physics Class 11 CBSE Study Material Full Chapter Download pdf-Anand Classes
What Is Uniform Circular Motion?
The movement of a body following a circular path is called a circular motion. Now, the motion of a body moving with constant speed along a circular path is called Uniform Circular Motion. Here, the speed is constant but the velocity changes.
If a particle is moving in a circle, it must have some acceleration acting towards the centre which is making it move around the centre. Since this acceleration is perpendicular to the velocity of a particle at every instant, it is only changing the direction of velocity and not magnitude and that’s why the motion is uniform circular motion. We call this acceleration centripetal acceleration (or radial acceleration), and the force acting towards the centre is called centripetal force.
In the case of uniform circular motion, the acceleration is:
ar = v2/r = ω2r
If the mass of the particle is m, we can say from the second law of motion that:
F = ma
mv2/r= mω2r
This is not a special force, actually force like tension or friction may be a cause of origination of centripetal force. When the vehicles turn on the roads, it is the frictional force between tyres and ground that provides the required centripetal force for turning.
What Is Circular Motion?
Circular motion is described as a movement of an object while rotating along a circular path. Circular motion can be either uniform or non-uniform. During uniform circular motion, the angular rate of rotation and speed will be constant, while during non-uniform motion the rate of rotation keeps changing.
Some of the most common examples of circular motion include man-made satellite that revolves around the earth, a rotating ceiling fan, a moving car’s wheel, the blades in a windmill, and gears in gas turbines.
A particle is said to execute circular motion when it moves along the circumference of a circular path. An important aspect of circular motion is that the direction of motion is changing continuously unlike in the case of linear motion. Hence, circular motion can also be described in terms of angular variables.
Angular Variables
Angular Displacement
It is defined as the angle turned by a rotating particle per unit time. It is represented by ∆θ and measured in radians.
Angular Velocity
It is defined as the rate of change in angular displacement of a particle in a circular motion. It is denoted by
ω = lim∆t→0 (∆θ/∆t) = dθ/dt
Angular velocity is measured in rad/s. Apart from angular velocity and angular speed, a particle in circular motion also possesses linear velocity and corresponding linear speed.
v= ds/dt
v= |ds/dt|; s is the displacement of the particle
Relation between Linear Speed(V) and Angular Speed(Ω)
In vector form
v= ω x r
Where r is the position vector of the particle measured with respect to the centre of the circle.
(Or)
v = rω
The acceleration of a particle in circular motion has two components:
- Tangential acceleration at: This is the component of acceleration in the direction of the velocity of the particle.
at= d|v|/dt
- Radial acceleration ar: This is the component of acceleration directed towards the centre of the circle. This component causes a change in the direction of the velocity of a particle in a circular motion.
ar= v2/r = rω2
Angular Acceleration
It is defined as the rate of change of angular velocity of the rotating particle. It is measured in rad/s2
α = dω/dt = d2θ/dt2
Circular motion can be uniform and non-uniform depending on the nature of acceleration of the particle. The motion is called uniform circular motion when the particle is moving along a circular path possessing a constant speed.
During circular motion, the velocity vector changes its direction at each point on the circle. This implies that the radial component of acceleration is always non-zero. The tangential component can take a positive or negative value in the case of non-uniform circular motion and a zero value in the case of uniform circular motion.
We understand that the acceleration of a particle in a circular motion is always directed towards the centre and is given by v2/r. Applying Newton’s second law of motion in this situation;
Fcen = mv2/r
Where m is the mass of the particle
Fc is the centripetal force directed towards the centre of the circular path.
Examples of centripetal forces include gravitational force, the tension in a string and friction.
NOTE
So if a particle is moving in a uniform circular motion:
1) Its speed is constant
2) Velocity is changing at every instant
3) There is no tangential acceleration
4) Radial (centripetal) acceleration = ω2r
5) v=ωr
In case of non-uniform circular motion, there is some tangential acceleration due to which the speed of the particle increases or decreases. The resultant acceleration is the vector sum of radial acceleration and tangential acceleration.
Uniform Circular Motion Examples
Following are the examples of uniform circular motion:
- Motion of artificial satellites around the earth is an example of uniform circular motion. The gravitational force from the earth makes the satellites stay in the circular orbit around the earth.
- The motion of electrons around its nucleus.
- The motion of blades of the windmills.
- The tip of second’s hand of a watch with a circular dial shows uniform circular motion.
Application of Newton’s Laws of Motion
Let us understand the application of Newton’s laws of motion in two different scenarios. The motion of a vehicle will be on either:
At Level Road
At an instant when a vehicle makes a turn on a level road, there are three different forces acting.
- The weight of the car W= mg
- Frictional force ff
- Normal reaction N
In the vertical direction N-mg = 0
N = mg
The centripetal acceleration for circular motion is provided by static friction. This friction holds back the vehicle from moving away from the circle.
ff = mv2/r ≤ µN
ff = mv2/r ≤ µ mg
µ is the coefficient of static friction
This implies that for a circular path of given radius and µ, there is a maximum possible speed of the vehicle.
Solved Problems
Question 1: What is the angular velocity of a particle in a circular orbit, rotating at the rate of 200 times per minute?
Solution: In the given problem, the frequency of rotation is 200 times per minute
ω= 2πf
= 2π x 200/60 = 20.93 rad/s
Question 2: An electrically powered wheel is rotating about its axis at the rate of 900 rotations per minute. When the power is turned off it comes it rest in 1 minute. Find the angular deceleration of the wheel in rad/s2.
Solution: From the laws of motion in the case of rotational motion, We know that ω = ω0 + αt.
From the given data :
ω0 = 900rpm = 900 x 2π/60 rad/s
ω = 0 and t= 60s
Hence, angular deceleration α = π/2
Question 3: A bus is moving in a circular track of radius 1000cm with a speed of 10m/s. A pendulum is suspended from the roof of the bus by a light rigid rod of length 100cm. Find the angle made by the rod with the track. (Use g=10m/s2).
Solution:
tan θ = v2/rg = 102/10×10
tan θ = 1
tan θ = 45⁰
Question 4: The minimum velocity with which a car driver must traverse a curve of radius 150 m and coefficient of friction 0.6 to avoid skidding is? [IIT-JEE 2002].
Solution: In the relation mv2/r =µN substitute N = mg
We get v2 =µrg
v2 = 0.6x150x10
v= 30m/s
Question 5: Which of the following statements is false for a particle moving in a circle with a constant angular speed? [AIEEE 2004]
a)The velocity vector is tangent to the circle
b) The acceleration vector is tangent to the circle
c) The acceleration vector points to the centre of the circle.
d) The velocity and acceleration vectors are perpendicular to each other.
Solution: Option b)
Frequently Asked Questions on Circular Motion
What type of motion is called circular motion?
The motion of an object in a circular path along the circumference of a circle or rotation along a circular path is called circular motion.
What are the types of circular motion?
Circular motion can be either uniform or non-uniform.
Give an example of circular motion.
The movement of the satellite in a circular orbit, ice skaters going in a circle with constant velocity, and cars moving in a circular path are examples of circular motion.
What is the value of instantaneous acceleration in a uniform circular motion?
The instantaneous acceleration in a uniform circular motion is given by
a = v2/R
v is the velocity of the object.
R is the radius of the circle.
The direction is perpendicular to velocity and directed inwards along the radius.
Name the device used for measuring the speed of rotation.
The tachometer is a device that is used for measuring the speed of rotation.
What happens to the velocity vector of a particle, if the particle is moving in a circle, at equal angles in equal times.
The velocity vector of a particle will change its direction. This is because it is always directed in the direction of the tangent to the circle.
Which property is conserved when a particle is moving with constant angular velocity?
When a particle is moving with constant angular velocity, the energy of the particle is conserved. This is because in a uniform circular motion, kinetic energy remains unchanged and the momentum of the particle varies with a change in velocity.
What happens to the direction when a vector is multiplied by a positive number?
The work done by the body when it moves along a circle with a constant speed is zero. This means that the work done by the centripetal force is zero.
circular motion, circular motion class 11, circular motion examples, circular motion definition, circular motion formula, circular motion class 11 notes, circular motion formula sheet, circular motion questions, circular motion class 11 formulas, circular motion neet questions, circular motion class 11, circular motion class 11 notes, circular motion class 11 formulas, circular motion class 11 questions, circular motion class 11 which chapter, circular motion class 11 ncert pdf, circular motion class 11 pdf, circular motion class 11 notes pdf, circular motion chapter name, circular motion class 11 neet questions, circular motion examples, circular motion equations, circular motion esaral, circular motion examples class 6, circular motion examples images, circular motion examples in real life, circular motion examples with pictures, circular motion explain, circular motion examples class 9, circular motion eg, circular motion laws of motion, circular motion lesson, circular motion lecture, circular motion linear speed, circular motion lesson plan, circular motion laws of motion class 11, circular motion lab, circular motion lab report, circular motion lever examples, circular motion linear velocity, circular motion by physics wallah, circular motion basic questions, circular motion banked road, circular motion basics, circular motion byjus, circular motion brushing technique, circular motion by mr sir, circular motion by nv sir, circular motion basic formulas, circular motion book pdf, circular motion all formulas, circular motion and rotational motion, circular motion and rotational motion difference, circular motion acceleration, circular motion all formulas jee, circular motion and rotational motion are same, circular motion animation, circular motion acceleration formula, circular motion also known as, circular motion and centripetal force, circular motion kya hota hai, circular motion ka example, circular motion kinematics, circular motion ka hindi, circular motion kise kahate hain, circular motion ki definition, circular motion ka definition, circular motion keywords, circular motion kya hai, circular motion ke example, circular motion notes, circular motion neet questions, circular motion neet pyq, circular motion notes pdf, circular motion ncert, circular motion numericals class 11, circular motion neet questions pdf, circular motion notes jee, circular motion numericals class 11 pdf, circular motion neet, circular motion of a car on a banked road, circular motion of a car on a level road, circular motion one shot, circular motion of a particle with constant speed is, circular motion on a banked road, circular motion of a car on a banked road class 11, circular motion of charged particle in magnetic field, circular motion of earth around the sun, circular motion on face, circular motion one example, circular motion formula, circular motion formula sheet, circular motion formula class 11, circular motion formula class 9, circular motion formula pdf, circular motion for class 6, circular motion face massage, circular motion formula sheet jee, circular motion force, circular motion formula derivation, circular motion definition, circular motion diagram, circular motion definition class 6, circular motion derivation, circular motion drawing, circular motion definition and examples, circular motion definition class 7, circular motion dpp, circular motion dimensions, circular motion definition in hindi, circular motion rotational motion, circular motion revision, circular motion real life examples, circular motion revision notes, circular motion radius formula, circular motion related questions, circular motion radius of curvature, circular motion radial and tangential acceleration, circular motion rectilinear, circular motion revolution equation, circular motion hcv solutions, circular motion hindi meaning, circular motion handwritten notes, circular motion hindi, circular motion hc verma solutions, circular motion hard questions, circular motion hair massage, circular motion head massage, circular motion horizontal and vertical, circular motion hyperphysics, circular motion gif, circular motion graph, circular motion give example, circular motion give two example, circular motion give one example, circular motion grade 9, circular motion grade 11 physics, circular motion grade 11, circular motion graph class 9, circular motion geogebra, circular motion in hindi, circular motion is a, circular motion is also known as, circular motion is in which chapter, circular motion images, circular motion is accelerated motion, circular motion is an example of, circular motion in vertical plane, circular motion is also called, circular motion is two dimensional, circular motion physics, circular motion practice problems, circular motion pyq jee mains, circular motion pyq neet, circular motion physics wallah, circular motion pictures, circular motion pdf, circular motion physics class 11, circular motion pyqs, circular motion photo, circular motion meaning in punjabi, circular motion meaning, circular motion meaning in hindi, circular motion mcq, circular motion massage, circular motion meaning in english, circular motion mind map, circular motion model, circular motion mcq neet, circular motion meaning in bengali, circular motion vs rotational motion, circular motion velocity formula, circular motion velocity, circular motion videos, circular motion vertical circle, circular motion vibrating screen, circular motion vedantu, circular motion velocity and acceleration, circular motion vertical, circular motion vectors, circular motion jee mains questions, circular motion jee notes, circular motion jee advanced questions, circular motion jee notes pdf, circular motion jee mains, circular motion jee mains notes, circular motion jee formula, circular motion jee quora, circular motion joint, circular motion daily life examples, circular motion questions, circular motion questions class 11, circular motion questions neet, circular motion questions and answers pdf, circular motion questions for jee, circular motion questions and answers pdf class 11, circular motion questions and answers, circular motion questions and answers class 11, circular motion question bank, circular motion questions toppr, circular motion which chapter, circular motion with example, circular motion weightage in jee, circular motion worksheets, circular motion working model, circular motion wikipedia, circular motion with constant speed, circular motion weightage in neet, circular motion what is, circular motion with friction, circular motion short notes, circular motion simulation, circular motion short definition, circular motion simple definition, circular motion short notes pdf, circular motion short notes jee, circular motion si unit, circular motion synonyms, circular motion speed formula, circular motion simulation phet, circular motion topics, circular motion two examples, circular motion to linear motion, circular motion types, circular motion toppr, circular motion time period, circular motion tangential acceleration, circular motion test, circular motion toppr questions, circular motion theory questions, circular motion x and y components, xkcd circular motion, tutor circular motion, circular motion examples, circular motion 5 examples, circular motion examples in real life, circular motion youtube, circular motion year 12, circle motion youtube, rotational motion youtube, circular motion previous year questions jee mains, circular motion previous year questions neet, circular motion previous year questions, circular motion previous year jee questions, circular motion physics youtube, circular motion x and y components, circular motion unit, circular motion uniform, circular motion unacademy, circular motion unacademy pdf, circular motion uniform and nonuniform, circular motion uniform velocity, circular motion up and down, circular motion university physics, circular motion unity, circular motion examples, circular motion zero acceleration, circular motion velocity zero, torque in circular motion zero, when is circular motion zero, physics circular motion, rotational motion zhongwen, circular motion is called, circular motion two examples, circular motion 5 examples, circular motion time formula
