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A particle performs uniform circular motion with an angular momentum l if the frequency of particles motion is tripled and the kinetic energy is doubled the angular momentum becomes what?
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A particle performs uniform circular motion with an angular momentum l...
Understanding Angular Momentum in Uniform Circular Motion
In uniform circular motion, the angular momentum (l) of a particle is given by the formula:
l = mvr
Where:
- m = mass of the particle
- v = linear velocity
- r = radius of the circular path
The linear velocity (v) can be related to the frequency (f) of the motion:
v = 2πrf
Effects of Tripling Frequency
When the frequency of the particle's motion is tripled (f' = 3f):
- The new linear velocity becomes:
- v' = 2πr(3f) = 6πrf = 3v
Thus, the new velocity is three times the original velocity.
Effects of Doubling Kinetic Energy
The kinetic energy (KE) of a particle in circular motion is given by:
KE = (1/2)mv²
If the kinetic energy is doubled (KE' = 2KE):
- Original KE = (1/2)m(v²)
- New KE = (1/2)m(v'²) = 2(1/2)m(v²)
Setting up this equality gives:
m(v'²) = 2mv² => v'² = 2v² => v' = √2 * v
Combining Effects on Angular Momentum
Now we need to analyze how both changes affect angular momentum:
1. New Linear Velocity:
- v' = √2 * v
2. New Angular Momentum:
- l' = m(v')r
- Substituting v' gives:
- l' = m(√2v)r = √2(mvr) = √2l
Conclusion
The new angular momentum when the frequency is tripled and the kinetic energy is doubled is:
- l' = √2l
Thus, the angular momentum becomes √2 times the original angular momentum.
In uniform circular motion, the angular momentum (l) of a particle is given by the formula:
l = mvr
Where:
- m = mass of the particle
- v = linear velocity
- r = radius of the circular path
The linear velocity (v) can be related to the frequency (f) of the motion:
v = 2πrf
Effects of Tripling Frequency
When the frequency of the particle's motion is tripled (f' = 3f):
- The new linear velocity becomes:
- v' = 2πr(3f) = 6πrf = 3v
Thus, the new velocity is three times the original velocity.
Effects of Doubling Kinetic Energy
The kinetic energy (KE) of a particle in circular motion is given by:
KE = (1/2)mv²
If the kinetic energy is doubled (KE' = 2KE):
- Original KE = (1/2)m(v²)
- New KE = (1/2)m(v'²) = 2(1/2)m(v²)
Setting up this equality gives:
m(v'²) = 2mv² => v'² = 2v² => v' = √2 * v
Combining Effects on Angular Momentum
Now we need to analyze how both changes affect angular momentum:
1. New Linear Velocity:
- v' = √2 * v
2. New Angular Momentum:
- l' = m(v')r
- Substituting v' gives:
- l' = m(√2v)r = √2(mvr) = √2l
Conclusion
The new angular momentum when the frequency is tripled and the kinetic energy is doubled is:
- l' = √2l
Thus, the angular momentum becomes √2 times the original angular momentum.
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A particle performs uniform circular motion with an angular momentum l if the frequency of particles motion is tripled and the kinetic energy is doubled the angular momentum becomes what?
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A particle performs uniform circular motion with an angular momentum l if the frequency of particles motion is tripled and the kinetic energy is doubled the angular momentum becomes what? 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 performs uniform circular motion with an angular momentum l if the frequency of particles motion is tripled and the kinetic energy is doubled the angular momentum becomes what? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle performs uniform circular motion with an angular momentum l if the frequency of particles motion is tripled and the kinetic energy is doubled the angular momentum becomes what?.
A particle performs uniform circular motion with an angular momentum l if the frequency of particles motion is tripled and the kinetic energy is doubled the angular momentum becomes what? 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 performs uniform circular motion with an angular momentum l if the frequency of particles motion is tripled and the kinetic energy is doubled the angular momentum becomes what? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle performs uniform circular motion with an angular momentum l if the frequency of particles motion is tripled and the kinetic energy is doubled the angular momentum becomes what?.
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