Q5. Rolling Angular Momentum NEET 2026 Important Model скачать в хорошем качестве

Q5. Rolling Angular Momentum NEET 2026 Important Model

To find the angular momentum of a rolling spherical shell about the origin, we must consider both its rotational motion about its center and its translational motion as a point mass relative to the origin.1. The Concept of Angular Momentum in RollingFor an object rolling without slipping, the total angular momentum ($L$) about a fixed point (the origin $O$) is the vector sum of two components:Translational Angular Momentum ($L_{trans}$): The momentum due to the center of mass ($CM$) moving at a distance from the origin.Rotational Angular Momentum ($L_{rot}$): The momentum due to the object spinning about its own center of mass.The Formula$$L_{total} = Mvr + I\omega$$$M$: Mass of the shell ($1 \text{ kg}$).$v$: Linear velocity of the center of mass.$r$: Radius of the shell (distance from the plane to the center).$I$: Moment of Inertia of the spherical shell.$\omega$: Angular speed.2. Key SubstitutionsTo solve the numerical, we apply the specific properties of a thin spherical shell and the condition of rolling:Moment of Inertia ($I$): For a hollow spherical shell, $I = \frac{2}{3}Mr^2$.Rolling Condition: For pure rolling, the linear velocity is linked to angular speed by $v = r\omega$.Deriving the Total MagnitudeSubstitute these into the main equation:$$L = M(r\omega)r + \left(\frac{2}{3}Mr^2\right)\omega$$$$L = Mr^2\omega + \frac{2}{3}Mr^2\omega$$Combine the terms:$$L = \left(1 + \frac{2}{3}\right)Mr^2\omega = \frac{5}{3}Mr^2\omega$$3. Solving for $a$The problem states that the magnitude of angular momentum is $\frac{a}{3}Mr^2\omega$. By comparing this to our derived formula:$$\frac{a}{3}Mr^2\omega = \frac{5}{3}Mr^2\omega$$By inspection:$a = 5 #NEETPhysics #RotationalMotion #PhysicsTricks #NEET2026 #PhysicsConcepts #AngularMomentum #MedicalEntrance #JEE #jeeaprilattempt #jeejanuaryattempt #jeeadvanced #mhtcetlatestupdates #kcet #rotationalmotion #education #physicstricks #SHORTCUTSINPHYSICS #physics #ncertsolutions #ncertphysics #neetncert#2025 Rank Saver #📉: Don't let tough Physics kill your rank again. •#2. @600# Elite Questions 🎯: Master 600 models; cover 100% concepts. •3. @#Target 150+ Marks 🏆: Lock in your score with surgical precision. •4. @#2-Hour Daily Limit ⏳: Max results in minimum time—save energy for Bio. •5. @#40-Day Masterplan 🗓️: 15 numericals a day to finish the entire syllabus. •6. @#Concept Clarity 💡: We teach the "Why," not just the solution. •7. @#Live Doubt Marathons 🏃‍♂️: Weekly live sessions to clear every hurdle. •8. @#5 Full PCB Mock Tests 📝: Realistic 720-mark practice for exam grit. •9. @#Darna Mana Hai 🛡️: Zero stress. One platform. Total confidence. 10. @#Just ₹2500 💎: Premium coaching at the best price. Watch demos now!