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A ballet dancer spins about a vertical axis at 2.5π rad/s with his both arms outstretched. With the arms folded, the moment of inertia about the same axis of rotation changes by 25%. Calculate the new speed of rotation in r.p.m.
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A ballet dancer spins about a vertical axis at 2.5π rad/s with his bot...
as arms are near the axis moment of inertia DECREASES by 25% also L=I*w therefore angular velocity decreases by 25% according to law of conservation of angular momentum.thus Ur answer is 125*2.5*π/100
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A ballet dancer spins about a vertical axis at 2.5π rad/s with his bot...
Calculating the New Speed of Rotation
- The initial angular speed of rotation, ω_initial = 2.5π rad/s
- The moment of inertia changes by 25%, so the new moment of inertia, I_new = 1.25 * I_initial

Conservation of Angular Momentum
- According to the law of conservation of angular momentum, the initial angular momentum = final angular momentum
- Initial angular momentum, L_initial = I_initial * ω_initial
- Final angular momentum, L_final = I_new * ω_final

Equating Initial and Final Angular Momentums
- Equating the initial and final angular momentums:
I_initial * ω_initial = I_new * ω_final
I_initial * 2.5π = 1.25 * I_initial * ω_final
2.5π = 1.25 * ω_final
ω_final = 2.5π / 1.25
ω_final = 2π rad/s

Converting to RPM
- The new speed of rotation in revolutions per minute (RPM) can be calculated by converting the angular speed from rad/s to RPM:
ω_final = 2π rad/s = 2π * 60 / 2π RPM
ω_final = 60 RPM
Therefore, the new speed of rotation with the arms folded is 60 RPM.
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A ballet dancer spins about a vertical axis at 2.5π rad/s with his both arms outstretched. With the arms folded, the moment of inertia about the same axis of rotation changes by 25%. Calculate the new speed of rotation in r.p.m.
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A ballet dancer spins about a vertical axis at 2.5π rad/s with his both arms outstretched. With the arms folded, the moment of inertia about the same axis of rotation changes by 25%. Calculate the new speed of rotation in r.p.m. for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A ballet dancer spins about a vertical axis at 2.5π rad/s with his both arms outstretched. With the arms folded, the moment of inertia about the same axis of rotation changes by 25%. Calculate the new speed of rotation in r.p.m. covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A ballet dancer spins about a vertical axis at 2.5π rad/s with his both arms outstretched. With the arms folded, the moment of inertia about the same axis of rotation changes by 25%. Calculate the new speed of rotation in r.p.m..
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