A uniform square plate of mass $2.0 \mathrm{~kg}$ and edge $10 \mathrm{~cm}$ rotates about one of its diagonals under the action of a constant torque of $0.10 \mathrm{~N}-\mathrm{m}$. Calculate the angular momentum and kinetic energy of the plate at the end of the fifth second after the start.
$\mathrm{T}=\mathrm{l \alpha}$
$0.1=\frac{\mathrm{Ma}^{2}}{12}(\alpha)$
$0.1=\frac{(2)(0.1)^{2}}{12}(\alpha)$
$\alpha=60 \mathrm{rad} / \mathrm{sec}$
$\omega_{0}=0, t=5 \mathrm{sec}$
$\omega=\omega_{0}+\alpha t$
Angular momentum , L= la
$=\frac{(2)(0.1)^{2}}{12}(300)$
$=\left[\begin{array}{l}\frac{m^{2}}{}\end{array}\right]$
$=0.5 \mathrm{~kg}-\mathrm{sec}$
$\mathrm{KE}=2$
$\mathrm{I} \omega^{2}$
$=\frac{1}{2}\left[\frac{(2)(0.1)^{2}}{12}\right](300)^{2}$
$=\frac{1}{2}\left[\frac{(2)(0.1)^{2}}{12}\right](300)^{2}$
$K E=75 \mathrm{~J}$
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- 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
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- Chemical Effects of Electric Current,