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The angular momentum of a particle relative to origin varies with time (r) as L-(4-atv) kgm²/s, where alpha = 1kg * m ^ 2 / (s ^ 3) The angle between L and the torque acting on the particle becomes 45° after a time of sec.?
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The angular momentum of a particle relative to origin varies with time...
Understanding Angular Momentum
Angular momentum (L) of a particle is given by the equation:
L = 4 - atv, where alpha (α) = 1 kg*m²/(s³).
This indicates that L varies with time (t) and velocity (v).
Torque and Its Relation to Angular Momentum
The torque (τ) acting on the particle is related to the change in angular momentum over time:
τ = dL/dt.
Given that L varies with time, we can find τ as follows:
- Differentiate L with respect to time to find the expression for torque.
Condition for Angle Between Torque and Angular Momentum
The angle (θ) between L and τ is given as 45°. At this angle, the relationship can be expressed as:
- τ = |τ| * cos(θ).
- Since θ = 45°, we have cos(45°) = 1/√2.
Finding Time When Angle Becomes 45°
To determine the time at which the angle between L and τ becomes 45°:
- Set up the equation based on the relationship between L and τ.
- Use the values given for α and the form of L to find the time at which this condition holds true.
Conclusion
The time at which the angle between the torque and angular momentum becomes 45° can be calculated by analyzing the equations governing L and τ. By differentiating L and evaluating the conditions for torque, one can deduce the specific time interval required for this alignment in vector directions.
This approach emphasizes understanding the physical significance of the relationship between torque and angular momentum in rotational dynamics, which is pivotal in various applications of physics.
Angular momentum (L) of a particle is given by the equation:
L = 4 - atv, where alpha (α) = 1 kg*m²/(s³).
This indicates that L varies with time (t) and velocity (v).
Torque and Its Relation to Angular Momentum
The torque (τ) acting on the particle is related to the change in angular momentum over time:
τ = dL/dt.
Given that L varies with time, we can find τ as follows:
- Differentiate L with respect to time to find the expression for torque.
Condition for Angle Between Torque and Angular Momentum
The angle (θ) between L and τ is given as 45°. At this angle, the relationship can be expressed as:
- τ = |τ| * cos(θ).
- Since θ = 45°, we have cos(45°) = 1/√2.
Finding Time When Angle Becomes 45°
To determine the time at which the angle between L and τ becomes 45°:
- Set up the equation based on the relationship between L and τ.
- Use the values given for α and the form of L to find the time at which this condition holds true.
Conclusion
The time at which the angle between the torque and angular momentum becomes 45° can be calculated by analyzing the equations governing L and τ. By differentiating L and evaluating the conditions for torque, one can deduce the specific time interval required for this alignment in vector directions.
This approach emphasizes understanding the physical significance of the relationship between torque and angular momentum in rotational dynamics, which is pivotal in various applications of physics.
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The angular momentum of a particle relative to origin varies with time (r) as L-(4-atv) kgm²/s, where alpha = 1kg * m ^ 2 / (s ^ 3) The angle between L and the torque acting on the particle becomes 45° after a time of sec.?
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The angular momentum of a particle relative to origin varies with time (r) as L-(4-atv) kgm²/s, where alpha = 1kg * m ^ 2 / (s ^ 3) The angle between L and the torque acting on the particle becomes 45° after a time of sec.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The angular momentum of a particle relative to origin varies with time (r) as L-(4-atv) kgm²/s, where alpha = 1kg * m ^ 2 / (s ^ 3) The angle between L and the torque acting on the particle becomes 45° after a time of sec.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The angular momentum of a particle relative to origin varies with time (r) as L-(4-atv) kgm²/s, where alpha = 1kg * m ^ 2 / (s ^ 3) The angle between L and the torque acting on the particle becomes 45° after a time of sec.?.
The angular momentum of a particle relative to origin varies with time (r) as L-(4-atv) kgm²/s, where alpha = 1kg * m ^ 2 / (s ^ 3) The angle between L and the torque acting on the particle becomes 45° after a time of sec.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The angular momentum of a particle relative to origin varies with time (r) as L-(4-atv) kgm²/s, where alpha = 1kg * m ^ 2 / (s ^ 3) The angle between L and the torque acting on the particle becomes 45° after a time of sec.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The angular momentum of a particle relative to origin varies with time (r) as L-(4-atv) kgm²/s, where alpha = 1kg * m ^ 2 / (s ^ 3) The angle between L and the torque acting on the particle becomes 45° after a time of sec.?.
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