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Two point masses m1=2kg and m2=3kg are connected by a pole of length 2m and mass 3kg and the axis of rotation pass through centre of mass of pole n is perpendicular to its length. what is the total moment of inertia of the system about the axis?
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Two point masses m1=2kg and m2=3kg are connected by a pole of length 2...
Understanding the System
In this problem, we have two point masses and a pole. We'll calculate the total moment of inertia of the system about the axis that passes through the center of mass of the pole.
Components of the System
- Mass of point mass m1 = 2 kg
- Mass of point mass m2 = 3 kg
- Length of the pole = 2 m
- Mass of the pole = 3 kg
Finding the Moment of Inertia
1. Moment of Inertia of Point Masses:
- The distance from the center of mass of the pole to m1 (left end) is 1 m (half the pole's length).
- The distance to m2 (right end) is also 1 m.
- Moment of inertia (I1) for m1:
- I1 = m1 * d1^2 = 2 kg * (1 m)^2 = 2 kg·m²
- Moment of inertia (I2) for m2:
- I2 = m2 * d2^2 = 3 kg * (1 m)^2 = 3 kg·m²
2. Moment of Inertia of the Pole:
- For a uniform pole of length L and mass m, the moment of inertia about its center is given by:
- I_pole = (1/12) * m * L^2
- Here, L = 2 m and m = 3 kg:
- I_pole = (1/12) * 3 kg * (2 m)^2 = 1 kg·m²
Total Moment of Inertia
- Total moment of inertia (I_total) = I1 + I2 + I_pole
- I_total = 2 kg·m² + 3 kg·m² + 1 kg·m² = 6 kg·m²
Conclusion
The total moment of inertia of the system about the axis through the center of mass of the pole is 6 kg·m².
In this problem, we have two point masses and a pole. We'll calculate the total moment of inertia of the system about the axis that passes through the center of mass of the pole.
Components of the System
- Mass of point mass m1 = 2 kg
- Mass of point mass m2 = 3 kg
- Length of the pole = 2 m
- Mass of the pole = 3 kg
Finding the Moment of Inertia
1. Moment of Inertia of Point Masses:
- The distance from the center of mass of the pole to m1 (left end) is 1 m (half the pole's length).
- The distance to m2 (right end) is also 1 m.
- Moment of inertia (I1) for m1:
- I1 = m1 * d1^2 = 2 kg * (1 m)^2 = 2 kg·m²
- Moment of inertia (I2) for m2:
- I2 = m2 * d2^2 = 3 kg * (1 m)^2 = 3 kg·m²
2. Moment of Inertia of the Pole:
- For a uniform pole of length L and mass m, the moment of inertia about its center is given by:
- I_pole = (1/12) * m * L^2
- Here, L = 2 m and m = 3 kg:
- I_pole = (1/12) * 3 kg * (2 m)^2 = 1 kg·m²
Total Moment of Inertia
- Total moment of inertia (I_total) = I1 + I2 + I_pole
- I_total = 2 kg·m² + 3 kg·m² + 1 kg·m² = 6 kg·m²
Conclusion
The total moment of inertia of the system about the axis through the center of mass of the pole is 6 kg·m².
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Two point masses m1=2kg and m2=3kg are connected by a pole of length 2m and mass 3kg and the axis of rotation pass through centre of mass of pole n is perpendicular to its length. what is the total moment of inertia of the system about the axis?
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Two point masses m1=2kg and m2=3kg are connected by a pole of length 2m and mass 3kg and the axis of rotation pass through centre of mass of pole n is perpendicular to its length. what is the total moment of inertia of the system about the axis? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Two point masses m1=2kg and m2=3kg are connected by a pole of length 2m and mass 3kg and the axis of rotation pass through centre of mass of pole n is perpendicular to its length. what is the total moment of inertia of the system about the axis? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two point masses m1=2kg and m2=3kg are connected by a pole of length 2m and mass 3kg and the axis of rotation pass through centre of mass of pole n is perpendicular to its length. what is the total moment of inertia of the system about the axis?.
Two point masses m1=2kg and m2=3kg are connected by a pole of length 2m and mass 3kg and the axis of rotation pass through centre of mass of pole n is perpendicular to its length. what is the total moment of inertia of the system about the axis? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Two point masses m1=2kg and m2=3kg are connected by a pole of length 2m and mass 3kg and the axis of rotation pass through centre of mass of pole n is perpendicular to its length. what is the total moment of inertia of the system about the axis? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two point masses m1=2kg and m2=3kg are connected by a pole of length 2m and mass 3kg and the axis of rotation pass through centre of mass of pole n is perpendicular to its length. what is the total moment of inertia of the system about the axis?.
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