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A ring of mass 15 kg and diameter 0.2 m is rotating about its geometrical axis at at 1800 rotations per minute its moment of inertia and angular momentum will be?
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A ring of mass 15 kg and diameter 0.2 m is rotating about its geometri...
Moment of Inertia Calculation
To calculate the moment of inertia (I) of a ring rotating about its geometrical axis, use the formula:
- I = m * r²
Where:
- m = mass of the ring = 15 kg
- r = radius of the ring = diameter / 2 = 0.2 m / 2 = 0.1 m
Now, substituting the values:
- I = 15 kg * (0.1 m)²
- I = 15 kg * 0.01 m²
- I = 0.15 kg·m²
Angular Momentum Calculation
Angular momentum (L) can be calculated using the formula:
- L = I * ω
Where:
- I = moment of inertia = 0.15 kg·m²
- ω = angular velocity in radians per second
To find ω, convert the rotations per minute (RPM) to radians per second:
- ω = 2 * π * (RPM / 60)
- ω = 2 * π * (1800 / 60)
- ω = 2 * π * 30
- ω ≈ 188.5 rad/s
Now, substituting into the angular momentum formula:
- L = 0.15 kg·m² * 188.5 rad/s
- L ≈ 28.28 kg·m²/s
Final Results
- Moment of Inertia (I): 0.15 kg·m²
- Angular Momentum (L): 28.28 kg·m²/s
This provides a detailed understanding of the moment of inertia and angular momentum for the given rotating ring.
To calculate the moment of inertia (I) of a ring rotating about its geometrical axis, use the formula:
- I = m * r²
Where:
- m = mass of the ring = 15 kg
- r = radius of the ring = diameter / 2 = 0.2 m / 2 = 0.1 m
Now, substituting the values:
- I = 15 kg * (0.1 m)²
- I = 15 kg * 0.01 m²
- I = 0.15 kg·m²
Angular Momentum Calculation
Angular momentum (L) can be calculated using the formula:
- L = I * ω
Where:
- I = moment of inertia = 0.15 kg·m²
- ω = angular velocity in radians per second
To find ω, convert the rotations per minute (RPM) to radians per second:
- ω = 2 * π * (RPM / 60)
- ω = 2 * π * (1800 / 60)
- ω = 2 * π * 30
- ω ≈ 188.5 rad/s
Now, substituting into the angular momentum formula:
- L = 0.15 kg·m² * 188.5 rad/s
- L ≈ 28.28 kg·m²/s
Final Results
- Moment of Inertia (I): 0.15 kg·m²
- Angular Momentum (L): 28.28 kg·m²/s
This provides a detailed understanding of the moment of inertia and angular momentum for the given rotating ring.
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A ring of mass 15 kg and diameter 0.2 m is rotating about its geometrical axis at at 1800 rotations per minute its moment of inertia and angular momentum will be?
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A ring of mass 15 kg and diameter 0.2 m is rotating about its geometrical axis at at 1800 rotations per minute its moment of inertia and angular momentum will be? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A ring of mass 15 kg and diameter 0.2 m is rotating about its geometrical axis at at 1800 rotations per minute its moment of inertia and angular momentum will be? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A ring of mass 15 kg and diameter 0.2 m is rotating about its geometrical axis at at 1800 rotations per minute its moment of inertia and angular momentum will be?.
A ring of mass 15 kg and diameter 0.2 m is rotating about its geometrical axis at at 1800 rotations per minute its moment of inertia and angular momentum will be? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A ring of mass 15 kg and diameter 0.2 m is rotating about its geometrical axis at at 1800 rotations per minute its moment of inertia and angular momentum will be? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A ring of mass 15 kg and diameter 0.2 m is rotating about its geometrical axis at at 1800 rotations per minute its moment of inertia and angular momentum will be?.
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