JEE Exam > JEE Questions > A uniform disc rotating in a horizontal plane...
Start Learning for Free
A uniform disc rotating in a horizontal plane about vertical axis passing through its center is 20 rpm has a body mass 2kg kept at its center if the mass now slides to the edge what would the angular speed the disc be? mass of disc is 5 kg?
Most Upvoted Answer
A uniform disc rotating in a horizontal plane about vertical axis pass...
Problem:
A uniform disc rotating in a horizontal plane about vertical axis passing through its center is 20 rpm has a body mass 2kg kept at its center if the mass now slides to the edge what would the angular speed the disc be? mass of disc is 5 kg?
Solution:
Given,
Initial angular speed of the disc, w1 = 20 rpm
Mass of the disc, m1 = 5 kg
Mass at the center of the disc, m2 = 2 kg
Final angular speed of the disc, w2 = ?
Conservation of Angular Momentum:
When the mass at the center of the disc slides to the edge, there is no external torque acting on the system. Hence, the angular momentum of the system remains conserved.
L1 = L2
Where, L1 = Initial angular momentum of the system
L2 = Final angular momentum of the system
Calculation of Initial Angular Momentum:
Initial angular momentum of the system can be calculated as follows:
L1 = I1 w1
Where, I1 = Moment of inertia of the disc about its axis
I1 = (1/2) m1 r1^2
Where, r1 = Radius of the disc
r1 = (1/2) x Diameter = (1/2) x 0.2 m = 0.1 m
I1 = (1/2) x 5 kg x (0.1 m)^2 = 0.025 kg.m^2
L1 = 0.025 kg.m^2 x (20 rpm x 2π/60) = 0.52 kg.m^2/s
Calculation of Final Angular Momentum:
Final angular momentum of the system can be calculated as follows:
L2 = I2 w2
Where, I2 = Moment of inertia of the disc about its axis with mass at the edge
I2 = (1/2) m1 r2^2 + m2 d^2
Where, r2 = Radius of the disc with mass at the edge
r2 = Diameter = 0.2 m
d = Distance of the mass from the axis of rotation
d = r2 = 0.2 m
I2 = (1/2) x 5 kg x (0.2 m)^2 + 2 kg x (0.2 m)^2 = 0.36 kg.m^2
L2 = 0.36 kg.m^2 x w2
Equating L1 and L2, we get:
0.52 = 0.36 w2
w2 = 1.44 rad/s
Therefore, the final angular speed of the disc will be 1.44 rad/s.
A uniform disc rotating in a horizontal plane about vertical axis passing through its center is 20 rpm has a body mass 2kg kept at its center if the mass now slides to the edge what would the angular speed the disc be? mass of disc is 5 kg?
Solution:
Given,
Initial angular speed of the disc, w1 = 20 rpm
Mass of the disc, m1 = 5 kg
Mass at the center of the disc, m2 = 2 kg
Final angular speed of the disc, w2 = ?
Conservation of Angular Momentum:
When the mass at the center of the disc slides to the edge, there is no external torque acting on the system. Hence, the angular momentum of the system remains conserved.
L1 = L2
Where, L1 = Initial angular momentum of the system
L2 = Final angular momentum of the system
Calculation of Initial Angular Momentum:
Initial angular momentum of the system can be calculated as follows:
L1 = I1 w1
Where, I1 = Moment of inertia of the disc about its axis
I1 = (1/2) m1 r1^2
Where, r1 = Radius of the disc
r1 = (1/2) x Diameter = (1/2) x 0.2 m = 0.1 m
I1 = (1/2) x 5 kg x (0.1 m)^2 = 0.025 kg.m^2
L1 = 0.025 kg.m^2 x (20 rpm x 2π/60) = 0.52 kg.m^2/s
Calculation of Final Angular Momentum:
Final angular momentum of the system can be calculated as follows:
L2 = I2 w2
Where, I2 = Moment of inertia of the disc about its axis with mass at the edge
I2 = (1/2) m1 r2^2 + m2 d^2
Where, r2 = Radius of the disc with mass at the edge
r2 = Diameter = 0.2 m
d = Distance of the mass from the axis of rotation
d = r2 = 0.2 m
I2 = (1/2) x 5 kg x (0.2 m)^2 + 2 kg x (0.2 m)^2 = 0.36 kg.m^2
L2 = 0.36 kg.m^2 x w2
Equating L1 and L2, we get:
0.52 = 0.36 w2
w2 = 1.44 rad/s
Therefore, the final angular speed of the disc will be 1.44 rad/s.
Attention JEE Students!
To make sure you are not studying endlessly, EduRev has designed JEE study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in JEE.
|
Explore Courses for JEE exam
|
|
Similar JEE Doubts
Top Courses for JEEView all
A uniform disc rotating in a horizontal plane about vertical axis passing through its center is 20 rpm has a body mass 2kg kept at its center if the mass now slides to the edge what would the angular speed the disc be? mass of disc is 5 kg?
Question Description
A uniform disc rotating in a horizontal plane about vertical axis passing through its center is 20 rpm has a body mass 2kg kept at its center if the mass now slides to the edge what would the angular speed the disc be? mass of disc is 5 kg? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A uniform disc rotating in a horizontal plane about vertical axis passing through its center is 20 rpm has a body mass 2kg kept at its center if the mass now slides to the edge what would the angular speed the disc be? mass of disc is 5 kg? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A uniform disc rotating in a horizontal plane about vertical axis passing through its center is 20 rpm has a body mass 2kg kept at its center if the mass now slides to the edge what would the angular speed the disc be? mass of disc is 5 kg?.
A uniform disc rotating in a horizontal plane about vertical axis passing through its center is 20 rpm has a body mass 2kg kept at its center if the mass now slides to the edge what would the angular speed the disc be? mass of disc is 5 kg? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A uniform disc rotating in a horizontal plane about vertical axis passing through its center is 20 rpm has a body mass 2kg kept at its center if the mass now slides to the edge what would the angular speed the disc be? mass of disc is 5 kg? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A uniform disc rotating in a horizontal plane about vertical axis passing through its center is 20 rpm has a body mass 2kg kept at its center if the mass now slides to the edge what would the angular speed the disc be? mass of disc is 5 kg?.
Solutions for A uniform disc rotating in a horizontal plane about vertical axis passing through its center is 20 rpm has a body mass 2kg kept at its center if the mass now slides to the edge what would the angular speed the disc be? mass of disc is 5 kg? in English & in Hindi are available as part of our courses for JEE.
Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of A uniform disc rotating in a horizontal plane about vertical axis passing through its center is 20 rpm has a body mass 2kg kept at its center if the mass now slides to the edge what would the angular speed the disc be? mass of disc is 5 kg? defined & explained in the simplest way possible. Besides giving the explanation of
A uniform disc rotating in a horizontal plane about vertical axis passing through its center is 20 rpm has a body mass 2kg kept at its center if the mass now slides to the edge what would the angular speed the disc be? mass of disc is 5 kg?, a detailed solution for A uniform disc rotating in a horizontal plane about vertical axis passing through its center is 20 rpm has a body mass 2kg kept at its center if the mass now slides to the edge what would the angular speed the disc be? mass of disc is 5 kg? has been provided alongside types of A uniform disc rotating in a horizontal plane about vertical axis passing through its center is 20 rpm has a body mass 2kg kept at its center if the mass now slides to the edge what would the angular speed the disc be? mass of disc is 5 kg? theory, EduRev gives you an
ample number of questions to practice A uniform disc rotating in a horizontal plane about vertical axis passing through its center is 20 rpm has a body mass 2kg kept at its center if the mass now slides to the edge what would the angular speed the disc be? mass of disc is 5 kg? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup