“Uniform and Non Uniform Circular Motion” MHT-CET Class 12 Physics Crash Course| Chapter Rotational Dynamics
In this session G.S. Khairnar will discuss the theory and MCQ’s of “Uniform and Non Uniform Circular Motion”. The session will be useful for all the aspirants of MHT-CET 2022. The session will be in Marathi and English.
Points to recall:
The linear motion of particle along the circumference of a circle is called Circular Motion. There are two types of circular motion.
Eg. Motion of tip of blades of clock, children enjoying the merry-g-round, motion of planets around the sun are some examples circular motion.
Radius Vector:- A vector drawn from the centre of circle to the position of the particle is called radius vector. It is directed away from the centre.
Angular Displacement:-The angle traced by radius vector in given time of interval at centre is called angular displacement of particle.
If particle completes one revolution in circular motion then
One radian is the angle subtended by an arc length equal to radius of the circle.
Instantaneous angular displacement is vector quantity.
Its direction is given by right hand rule.
Angular velocity: – The rate of change of the angular displacement with time is called angular velocity.
S.I. unit is rad/s.
Dimensions are [M0L0T-1θ1]
It is vector quantity. Its direction is determined by right hand rule.
Angular Acceleration:-The rate of change of angular velocity with time .OR change in angular velocity per unit time is called angular acceleration.
S.I. unit is rad/s Dimensions are [M0L0T-2]
It is vector quantity. Its direction is determined by right hand rule. In UCM angular acceleration is equal to zero.
Right Hand Rule: – Imagine the axis of rotation to be held in the right hand with curled fingers round the axis and the thumb stretched along the axis. If the curled fingers indicate the sense of circular motion the stretched thumb indicates the direction of angular displacement, angular velocity, angular acceleration.
There are two types of circular motion.
- Uniform circular motion.
- Non uniform circular motion.
(A) Uniform Circular Motion: The motion of particle along the circumference of a circle with constant angular velocity (linear speed).
In this case only direction of linear velocity changes with respect time, whereas the magnitude of linear velocity and angular velocity remains constant.
e.g. motion of every particle of blade of fan, motion of rotation of planets, motion of electrons around the nucleus are some important examples of uniform circular motion.
The centripetal acceleration required for maintaining the uniform circular motion is given as,
(B) Non-Uniform Circular Motion: The motion of particle along the circumference of a circle with the variable angular speed (linear speed).
e.g. imagine that the children enjoying the ride in giant wheel, which moves in vertical plane with the surface of earth. In this case the velocity of every single child is changing with respect to time.
The acceleration is always along or opposite to the linear velocity which maintains the non uniform circular motion. This acceleration is known as tangential acceleration. So the component of acceleration is given as,
:- Important Notes :-
- As angular velocity increase, the angular acceleration is vertically in upward direction
- As angular velocity decreases, angular acceleration is vertically in downward direction.
- Period of second hand is 60 s.
- Period of minute hand is 1 hour = 3600 s.
- Period of hour hand = 12 X 3600 s.
- Period of earth about own axis = 20 X 3600s.
- Period of earth round the sun
- T = 365 X 24 X 3600 s.
- Period of moon round the earth = 27.3 days
- Angular speed of second hand= 0.1047 rad/s.
- Angular speed of minute hand= 1.744 X103 rad/s
- Angular speed of hour hand =1.453 X 104rad/s.
Uniform and Non Uniform Circular Motion
Let’s solve the following MCQs
Q.1) The uniform circular motion is one in which…..
a) magnitude and direction of linear velocity is constant
b) only magnitude is of linear velocity is constant
c) only direction of linear velocity is constant
d) both ‘b’ and ‘c’
Answer
b) only magnitude is of linear velocity is constant
Q.2) Direction of angular displacement can be derived from
a) right hand screw rule
b) left hand screw rule
c) chain rule
d) both ‘b’ and ‘c’
Answer
a) right hand screw rule
Q.3) The magnitude of centripetal acceleration in uniform circular motion is given as,
Q.4) The component of acceleration along or opposite to direction of velocity in non uniform circular motion is,
a) radial acceleration
b) centripetal acceleration
c) tangential acceleration
c) angular acceleration
Answer
c) tangential acceleration
Q.5) Radial component of acceleration is non uniform circular motion is…..
Q.6) The direction of angular acceleration in decreasing non uniform motion is..
Q.7) The direction of angular acceleration in increasing non uniform motion is..
Q.8) Angular speed and linear speed of chair of giant wheel of radius 2.5 m rotating at the rate of 30 rpm
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