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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)?
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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
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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).
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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)?
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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)?.
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