NEET Exam > NEET Questions > A particle is moving with constant speed v al...
Start Learning for Free
A particle is moving with constant speed v along x-axis in positive direction. Find the angular velocity of the particle about the point (0,b), when positon of the particle is (a,0)?
Most Upvoted Answer
A particle is moving with constant speed v along x-axis in positive di...
Angular velocity=perpendicular component of velocity/radius=v[b/(a²+b²)^1/2]÷(a²+b²)^1/2=vb/a²+b²
Community Answer
A particle is moving with constant speed v along x-axis in positive di...
Position and Velocity Vectors:
When a particle is moving along the x-axis with a constant speed v, its position vector can be written as r = (a, 0), where a is the x-coordinate of the particle. Similarly, its velocity vector can be written as v = (v, 0), where v is the magnitude of the velocity.
Angular Velocity:
The angular velocity of a particle is the rate at which its position vector changes with respect to time. It is given by the cross product of the position vector and the velocity vector divided by the magnitude of the position vector squared.
Calculating Angular Velocity:
To find the angular velocity of the particle about the point (0, b), we need to calculate the cross product of the position vector r and the velocity vector v.
r x v = | i j k |
| a 0 0 |
| v 0 0 |
The cross product of the position vector r and the velocity vector v gives us a vector in the z-direction, since there is no component in the y-direction. Therefore, the z-component of the cross product is given by (0 * 0) - (0 * v) = 0.
The magnitude of the position vector squared is given by |r|^2 = a^2 + 0^2 = a^2.
So, the angular velocity of the particle about the point (0, b) is given by:
ω = (r x v) / |r|^2 = 0 / a^2 = 0
Conclusion:
The angular velocity of the particle about the point (0, b) is zero. This means that the particle is moving in a straight line along the x-axis and there is no rotation about the point (0, b).
When a particle is moving along the x-axis with a constant speed v, its position vector can be written as r = (a, 0), where a is the x-coordinate of the particle. Similarly, its velocity vector can be written as v = (v, 0), where v is the magnitude of the velocity.
Angular Velocity:
The angular velocity of a particle is the rate at which its position vector changes with respect to time. It is given by the cross product of the position vector and the velocity vector divided by the magnitude of the position vector squared.
Calculating Angular Velocity:
To find the angular velocity of the particle about the point (0, b), we need to calculate the cross product of the position vector r and the velocity vector v.
r x v = | i j k |
| a 0 0 |
| v 0 0 |
The cross product of the position vector r and the velocity vector v gives us a vector in the z-direction, since there is no component in the y-direction. Therefore, the z-component of the cross product is given by (0 * 0) - (0 * v) = 0.
The magnitude of the position vector squared is given by |r|^2 = a^2 + 0^2 = a^2.
So, the angular velocity of the particle about the point (0, b) is given by:
ω = (r x v) / |r|^2 = 0 / a^2 = 0
Conclusion:
The angular velocity of the particle about the point (0, b) is zero. This means that the particle is moving in a straight line along the x-axis and there is no rotation about the point (0, b).
Attention NEET Students!
To make sure you are not studying endlessly, EduRev has designed NEET study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in NEET.
|
Explore Courses for NEET exam
|
|
Similar NEET Doubts
Top Courses for NEETView all
A particle is moving with constant speed v along x-axis in positive direction. Find the angular velocity of the particle about the point (0,b), when positon of the particle is (a,0)?
Question Description
A particle is moving with constant speed v along x-axis in positive direction. Find the angular velocity of the particle about the point (0,b), when positon of the particle is (a,0)? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A particle is moving with constant speed v along x-axis in positive direction. Find the angular velocity of the particle about the point (0,b), when positon of the particle is (a,0)? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle is moving with constant speed v along x-axis in positive direction. Find the angular velocity of the particle about the point (0,b), when positon of the particle is (a,0)?.
A particle is moving with constant speed v along x-axis in positive direction. Find the angular velocity of the particle about the point (0,b), when positon of the particle is (a,0)? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A particle is moving with constant speed v along x-axis in positive direction. Find the angular velocity of the particle about the point (0,b), when positon of the particle is (a,0)? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle is moving with constant speed v along x-axis in positive direction. Find the angular velocity of the particle about the point (0,b), when positon of the particle is (a,0)?.
Solutions for A particle is moving with constant speed v along x-axis in positive direction. Find the angular velocity of the particle about the point (0,b), when positon of the particle is (a,0)? in English & in Hindi are available as part of our courses for NEET.
Download more important topics, notes, lectures and mock test series for NEET Exam by signing up for free.
Here you can find the meaning of A particle is moving with constant speed v along x-axis in positive direction. Find the angular velocity of the particle about the point (0,b), when positon of the particle is (a,0)? defined & explained in the simplest way possible. Besides giving the explanation of
A particle is moving with constant speed v along x-axis in positive direction. Find the angular velocity of the particle about the point (0,b), when positon of the particle is (a,0)?, a detailed solution for A particle is moving with constant speed v along x-axis in positive direction. Find the angular velocity of the particle about the point (0,b), when positon of the particle is (a,0)? has been provided alongside types of A particle is moving with constant speed v along x-axis in positive direction. Find the angular velocity of the particle about the point (0,b), when positon of the particle is (a,0)? theory, EduRev gives you an
ample number of questions to practice A particle is moving with constant speed v along x-axis in positive direction. Find the angular velocity of the particle about the point (0,b), when positon of the particle is (a,0)? tests, examples and also practice NEET tests.
|
|
Explore Courses for NEET 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