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Angular frequency of fan increases from 30 rpm to 60 rpm in pie sec .a dust particle is present at distance of 20 cm from axis of rotation. The tangential acceleration of particle in pie sec?
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Angular frequency of fan increases from 30 rpm to 60 rpm in pie sec .a...
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Angular frequency of fan increases from 30 rpm to 60 rpm in pie sec .a...
A. Given data:
- Initial angular frequency (ω₁) = 30 rpm
- Final angular frequency (ω₂) = 60 rpm
- Time taken (t) = π seconds
- Distance from axis of rotation (r) = 20 cm
B. Conversion of angular frequency:
We need to convert the angular frequency from rpm to rad/s.
- 1 revolution = 2π radians
- 1 minute = 60 seconds
So, the initial angular frequency (ω₁) in rad/s = (30 rpm) * (2π rad/1 revolution) * (1/60 min) * (1 min/60 s) = π rad/s
Similarly, the final angular frequency (ω₂) in rad/s = (60 rpm) * (2π rad/1 revolution) * (1/60 min) * (1 min/60 s) = 2π rad/s
C. Calculation of angular acceleration:
Angular acceleration (α) can be calculated using the formula:
α = (ω₂ - ω₁) / t
Substituting the values, we get:
α = (2π rad/s - π rad/s) / π s = π rad/s²
D. Calculation of tangential acceleration:
Tangential acceleration (at) can be calculated using the formula:
at = α * r
Substituting the values, we get:
at = π rad/s² * 20 cm = 20π cm/s²
E. Conversion of tangential acceleration:
Since the distance is given in centimeters, we can convert the tangential acceleration to meters by dividing it by 100.
at = 20π cm/s² * (1 m/100 cm) = 0.2π m/s²
F. Final answer:
The tangential acceleration of the dust particle is 0.2π m/s².
- Initial angular frequency (ω₁) = 30 rpm
- Final angular frequency (ω₂) = 60 rpm
- Time taken (t) = π seconds
- Distance from axis of rotation (r) = 20 cm
B. Conversion of angular frequency:
We need to convert the angular frequency from rpm to rad/s.
- 1 revolution = 2π radians
- 1 minute = 60 seconds
So, the initial angular frequency (ω₁) in rad/s = (30 rpm) * (2π rad/1 revolution) * (1/60 min) * (1 min/60 s) = π rad/s
Similarly, the final angular frequency (ω₂) in rad/s = (60 rpm) * (2π rad/1 revolution) * (1/60 min) * (1 min/60 s) = 2π rad/s
C. Calculation of angular acceleration:
Angular acceleration (α) can be calculated using the formula:
α = (ω₂ - ω₁) / t
Substituting the values, we get:
α = (2π rad/s - π rad/s) / π s = π rad/s²
D. Calculation of tangential acceleration:
Tangential acceleration (at) can be calculated using the formula:
at = α * r
Substituting the values, we get:
at = π rad/s² * 20 cm = 20π cm/s²
E. Conversion of tangential acceleration:
Since the distance is given in centimeters, we can convert the tangential acceleration to meters by dividing it by 100.
at = 20π cm/s² * (1 m/100 cm) = 0.2π m/s²
F. Final answer:
The tangential acceleration of the dust particle is 0.2π m/s².
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Angular frequency of fan increases from 30 rpm to 60 rpm in pie sec .a dust particle is present at distance of 20 cm from axis of rotation. The tangential acceleration of particle in pie sec?
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Angular frequency of fan increases from 30 rpm to 60 rpm in pie sec .a dust particle is present at distance of 20 cm from axis of rotation. The tangential acceleration of particle in pie sec? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Angular frequency of fan increases from 30 rpm to 60 rpm in pie sec .a dust particle is present at distance of 20 cm from axis of rotation. The tangential acceleration of particle in pie sec? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Angular frequency of fan increases from 30 rpm to 60 rpm in pie sec .a dust particle is present at distance of 20 cm from axis of rotation. The tangential acceleration of particle in pie sec?.
Angular frequency of fan increases from 30 rpm to 60 rpm in pie sec .a dust particle is present at distance of 20 cm from axis of rotation. The tangential acceleration of particle in pie sec? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Angular frequency of fan increases from 30 rpm to 60 rpm in pie sec .a dust particle is present at distance of 20 cm from axis of rotation. The tangential acceleration of particle in pie sec? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Angular frequency of fan increases from 30 rpm to 60 rpm in pie sec .a dust particle is present at distance of 20 cm from axis of rotation. The tangential acceleration of particle in pie sec?.
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