A boy is standing on a platform which is free to rotate about its axis. The boy holds an open umbrella coincides with that of the platform. The moment of inertia of " the platform plus the boy system" is $3.0$
$\times 10^{-3} \mathrm{~kg}_{-} \mathrm{m}^{2}$ and that of the umbrella is $2.0^{\times} 10^{-3} \mathrm{~kg}^{-} \mathrm{m}^{2}$. The boy starts spinning the umbrella about the axis at an angular speed of $2.0 \mathrm{rev} / \mathrm{s}$ with respect to himself. Find the angular velocity imparted to the platform.
Since, $\tau_{\text {ext }}=0$
$\therefore L_{i}=L_{f}$
$0+0=L_{\text {boy-final }}+L_{u m b-f \text { inal }}-(\mathrm{i})$
So, Angular speed of umbrella with respect to boy will be in the opposite direction. Let angular speed of boy be $\omega$
Now, $\omega_{u m b-d i s c}=\omega_{u m b}-\omega_{d i s c}$
$-2=\omega_{u m b}-\omega$
$\omega_{u m b}=\omega-2$
In equation (i),
$0=\left(3 \times 10^{-3}\right)(\omega)+\left(2 \times 10^{-3}\right)(\omega-2)$
$\omega=0.8 \mathrm{rev} / \mathrm{sec}$
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All Study Material
- JEE Main
- Exam Pattern
- Previous Year Papers
- PYQ Chapterwise
- Physics
- Kinematics 1D
- Kinemetics 2D
- Friction
- Work, Power, Energy
- Centre of Mass and Collision
- Rotational Dynamics
- Gravitation
- Calorimetry
- Elasticity
- Thermal Expansion
- Heat Transfer
- Kinetic Theory of Gases
- Thermodynamics
- Simple Harmonic Motion
- Wave on String
- Sound waves
- Fluid Mechanics
- Electrostatics
- Current Electricity
- Capacitor
- Magnetism and Matter
- Electromagnetic Induction
- Atomic Structure
- Dual Nature of Matter
- Nuclear Physics
- Radioactivity
- Semiconductors
- Communication System
- Error in Measurement & instruments
- Alternating Current
- Electromagnetic Waves
- Wave Optics
- X-Rays
- All Subjects
- Physics
- Motion in a Plane
- Law of Motion
- Work, Energy and Power
- Systems of Particles and Rotational Motion
- Gravitation
- Mechanical Properties of Solids
- Mechanical Properties of Fluids
- Thermal Properties of matter
- Thermodynamics
- Kinetic Theory
- Oscillations
- Waves
- Electric Charge and Fields
- Electrostatic Potential and Capacitance
- Current Electricity
- Thermoelectric Effects of Electric Current
- Heating Effects of Electric Current
- Moving Charges and Magnetism
- Magnetism and Matter
- Electromagnetic Induction
- Alternating Current
- Electromagnetic Wave
- Ray Optics and Optical Instruments
- Wave Optics
- Dual Nature of Radiation and Matter
- Atoms
- Nuclei
- Semiconductor Electronics: Materials, Devices and Simple Circuits.
- Chemical Effects of Electric Current,