Two particles of masses $m_{1}$ and $m_{2}$ are joined by a light rigid rod of length $r$. The system rotates at an angular speed $\omega$ about an axis through the centre of mass of the system and perpendicular to the rod. Show that the angular momentum of the system is $L=\mu r^{2} \omega$ where $\mu$ is the reduced mass of the system defined as
$\mu=\frac{m_{1} m_{2}}{m_{n}+m_{2}}$
Distance of COM from $m_{1}$ will be $r_{1}=\frac{m_{2} r}{\left(m_{1}+m_{2}\right)}$ Distance of COM from $m_{2}$ will be $r_{2}=\frac{m_{1} r}{\left(m_{1}+m_{2}\right)}$
$\mathrm{L}=\mid \omega$
$\mathrm{L}=\left(m_{1} r_{1}^{2}+m_{2} r_{2}^{2}\right) \omega$
$\mathrm{L}=\left[m_{1}\left(\frac{m_{2} r}{\left(m_{1}+m_{2}\right)}\right)^{2}+m_{2}\left(\frac{m_{1} r}{\left(m_{1}+m_{2}\right)}\right)^{2}\right]$
$\mathrm{L}=\mu r^{2} \omega$ where $\mu=\frac{m_{1} m_{2}}{m_{1}+m_{2}}$
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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,