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A rigid horizontal smooth rod AB of mass 0.75kg and length 40cm can rotate freely vertical axis through its midpoint O .Two rings each of mass 1kg initially at rest are placed at a distance of 10cm from O on either side of the rod .The rod is set in rotation with an angular velocity of 30 radian per second and when the rings reach the ends of the rod, the angular velocity in rad/sec is?
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Problem: Find the angular velocity of the rod when the rings reach the ends of the rod.
Given:
- Mass of the rod (m1) = 0.75 kg
- Length of the rod (l) = 40 cm = 0.4 m
- Distance of the rings from the midpoint (r) = 10 cm = 0.1 m
- Mass of each ring (m2) = 1 kg
- Initial angular velocity of the rod (ωi) = 30 rad/s
Solution:
We can solve this problem using the conservation of angular momentum. The total angular momentum of the system remains constant before and after the rings reach the ends of the rod.
Step 1: Find the moment of inertia of the rod about its midpoint.
- Moment of inertia of the rod (I1) = (1/12) x m1 x l2
- I1 = (1/12) x 0.75 x 0.42
- I1 = 0.005 m2kg
Step 2: Find the moment of inertia of the rings about the midpoint.
- Moment of inertia of each ring (I2) = m2 x r2
- I2 = 1 x 0.12
- I2 = 0.01 m2kg
Step 3: Find the initial angular momentum of the system.
- Initial angular momentum (Li) = I1 x ωi + 2I2 x ωi
- Li = 0.005 x 30 + 2 x 0.01 x 30
- Li = 1.5 kg m2/s
Step 4: Find the final moment of inertia of the system.
- Final moment of inertia (If) = I1 + 2I2
- If = 0.005 + 2 x 0.01
- If = 0.025 m2kg
Step 5: Find the final angular velocity of the system.
- Final angular momentum (Lf) = Li = If x ωf
- ωf = Li / If
- ωf = 1.5 / 0.
Given:
- Mass of the rod (m1) = 0.75 kg
- Length of the rod (l) = 40 cm = 0.4 m
- Distance of the rings from the midpoint (r) = 10 cm = 0.1 m
- Mass of each ring (m2) = 1 kg
- Initial angular velocity of the rod (ωi) = 30 rad/s
Solution:
We can solve this problem using the conservation of angular momentum. The total angular momentum of the system remains constant before and after the rings reach the ends of the rod.
Step 1: Find the moment of inertia of the rod about its midpoint.
- Moment of inertia of the rod (I1) = (1/12) x m1 x l2
- I1 = (1/12) x 0.75 x 0.42
- I1 = 0.005 m2kg
Step 2: Find the moment of inertia of the rings about the midpoint.
- Moment of inertia of each ring (I2) = m2 x r2
- I2 = 1 x 0.12
- I2 = 0.01 m2kg
Step 3: Find the initial angular momentum of the system.
- Initial angular momentum (Li) = I1 x ωi + 2I2 x ωi
- Li = 0.005 x 30 + 2 x 0.01 x 30
- Li = 1.5 kg m2/s
Step 4: Find the final moment of inertia of the system.
- Final moment of inertia (If) = I1 + 2I2
- If = 0.005 + 2 x 0.01
- If = 0.025 m2kg
Step 5: Find the final angular velocity of the system.
- Final angular momentum (Lf) = Li = If x ωf
- ωf = Li / If
- ωf = 1.5 / 0.
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A rigid horizontal smooth rod AB of mass 0.75kg and length 40cm can rotate freely vertical axis through its midpoint O .Two rings each of mass 1kg initially at rest are placed at a distance of 10cm from O on either side of the rod .The rod is set in rotation with an angular velocity of 30 radian per second and when the rings reach the ends of the rod, the angular velocity in rad/sec is?
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A rigid horizontal smooth rod AB of mass 0.75kg and length 40cm can rotate freely vertical axis through its midpoint O .Two rings each of mass 1kg initially at rest are placed at a distance of 10cm from O on either side of the rod .The rod is set in rotation with an angular velocity of 30 radian per second and when the rings reach the ends of the rod, the angular velocity in rad/sec is? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A rigid horizontal smooth rod AB of mass 0.75kg and length 40cm can rotate freely vertical axis through its midpoint O .Two rings each of mass 1kg initially at rest are placed at a distance of 10cm from O on either side of the rod .The rod is set in rotation with an angular velocity of 30 radian per second and when the rings reach the ends of the rod, the angular velocity in rad/sec is? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A rigid horizontal smooth rod AB of mass 0.75kg and length 40cm can rotate freely vertical axis through its midpoint O .Two rings each of mass 1kg initially at rest are placed at a distance of 10cm from O on either side of the rod .The rod is set in rotation with an angular velocity of 30 radian per second and when the rings reach the ends of the rod, the angular velocity in rad/sec is?.
A rigid horizontal smooth rod AB of mass 0.75kg and length 40cm can rotate freely vertical axis through its midpoint O .Two rings each of mass 1kg initially at rest are placed at a distance of 10cm from O on either side of the rod .The rod is set in rotation with an angular velocity of 30 radian per second and when the rings reach the ends of the rod, the angular velocity in rad/sec is? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A rigid horizontal smooth rod AB of mass 0.75kg and length 40cm can rotate freely vertical axis through its midpoint O .Two rings each of mass 1kg initially at rest are placed at a distance of 10cm from O on either side of the rod .The rod is set in rotation with an angular velocity of 30 radian per second and when the rings reach the ends of the rod, the angular velocity in rad/sec is? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A rigid horizontal smooth rod AB of mass 0.75kg and length 40cm can rotate freely vertical axis through its midpoint O .Two rings each of mass 1kg initially at rest are placed at a distance of 10cm from O on either side of the rod .The rod is set in rotation with an angular velocity of 30 radian per second and when the rings reach the ends of the rod, the angular velocity in rad/sec is?.
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