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A cord is wound around the circumference of wheel of radius "r" the axis of the wheel is horizontal and moment of inertia about it is "I" the weight "mg" is attached to the end of the cord and falls from rest . After falling through a distance"h" the angular velocity of the wheel will be.?
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Analysis of the Problem
To determine the angular velocity of the wheel after the weight falls through a distance "h", we can use the principle of conservation of mechanical energy. The weight attached to the cord will convert its potential energy into rotational kinetic energy of the wheel as it falls.
Conservation of Mechanical Energy
The initial potential energy of the weight is given by the equation:
E_potential_initial = mgh
As the weight falls, it will cause the wheel to rotate. The final rotational kinetic energy of the wheel is given by the equation:
E_rotational_final = (1/2)Iω^2
According to the principle of conservation of mechanical energy, the initial potential energy is equal to the final rotational kinetic energy:
mgh = (1/2)Iω^2
Deriving the Angular Velocity
To solve for the angular velocity (ω), we rearrange the equation:
ω^2 = (2mgh) / I
Taking the square root of both sides, we get:
ω = sqrt((2mgh) / I)
Therefore, the angular velocity of the wheel after the weight falls through a distance "h" is given by:
ω = sqrt((2mgh) / I)
Conclusion
The angular velocity of the wheel can be determined using the principle of conservation of mechanical energy. By equating the initial potential energy of the weight to the final rotational kinetic energy of the wheel, we can solve for the angular velocity. The equation for the angular velocity is ω = sqrt((2mgh) / I), where m is the mass of the weight, g is the acceleration due to gravity, h is the distance fallen, and I is the moment of inertia of the wheel about its axis.
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A cord is wound around the circumference of wheel of radius "r" the axis of the wheel is horizontal and moment of inertia about it is "I" the weight "mg" is attached to the end of the cord and falls from rest . After falling through a distance"h" the angular velocity of the wheel will be.?
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A cord is wound around the circumference of wheel of radius "r" the axis of the wheel is horizontal and moment of inertia about it is "I" the weight "mg" is attached to the end of the cord and falls from rest . After falling through a distance"h" the angular velocity of the wheel will be.? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A cord is wound around the circumference of wheel of radius "r" the axis of the wheel is horizontal and moment of inertia about it is "I" the weight "mg" is attached to the end of the cord and falls from rest . After falling through a distance"h" the angular velocity of the wheel will be.? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cord is wound around the circumference of wheel of radius "r" the axis of the wheel is horizontal and moment of inertia about it is "I" the weight "mg" is attached to the end of the cord and falls from rest . After falling through a distance"h" the angular velocity of the wheel will be.?.
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